All Publications

2023

Bläsius, Thomas; Friedrich, Tobias; Krejca, Martin S.; Molitor, Louise The Impact of Geometry on Monochrome Regions in the Flip Schelling ProcessComputational Geometry (CGTA) 2023: 101902
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Schelling's classical segregation model gives a coherent explanation for the wide-spread phenomenon of residential segregation. We introduce an agent-based saturated open-city variant, the Flip Schelling Process (FSP), in which agents, placed on a graph, have one out of two types and, based on the predominant type in their neighborhood, decide whether to change their types; similar to a new agent arriving as soon as another agent leaves the vertex. We investigate the probability that an edge u,v is monochrome, i.e., that both vertices u and v have the same type in the FSP, and we provide a general framework for analyzing the influence of the underlying graph topology on residential segregation. In particular, for two adjacent vertices, we show that a highly decisive common neighborhood, i.e., a common neighborhood where the absolute value of the difference between the number of vertices with different types is high, supports segregation and, moreover, that large common neighborhoods are more decisive. As an application, we study the expected behavior of the FSP on two common random graph models with and without geometry: (1) For random geometric graphs, we show that the existence of an edge u,v makes a highly decisive common neighborhood for u and v more likely. Based on this, we prove the existence of a constant c>0 such that the expected fraction of monochrome edges after the FSP is at least 1/2+c. (2) For Erdős–Rényi graphs we show that large common neighborhoods are unlikely and that the expected fraction of monochrome edges after the FSP is at most 1/2+o(1). Our results indicate that the cluster structure of the underlying graph has a significant impact on the obtained segregation strength.
@article{blasius2023impact, abstract = {Schelling's classical segregation model gives a coherent explanation for the wide-spread phenomenon of residential segregation. We introduce an agent-based saturated open-city variant, the Flip Schelling Process (FSP), in which agents, placed on a graph, have one out of two types and, based on the predominant type in their neighborhood, decide whether to change their types; similar to a new agent arriving as soon as another agent leaves the vertex. We investigate the probability that an edge {u,v} is monochrome, i.e., that both vertices u and v have the same type in the FSP, and we provide a general framework for analyzing the influence of the underlying graph topology on residential segregation. In particular, for two adjacent vertices, we show that a highly decisive common neighborhood, i.e., a common neighborhood where the absolute value of the difference between the number of vertices with different types is high, supports segregation and, moreover, that large common neighborhoods are more decisive. As an application, we study the expected behavior of the FSP on two common random graph models with and without geometry: (1) For random geometric graphs, we show that the existence of an edge {u,v} makes a highly decisive common neighborhood for u and v more likely. Based on this, we prove the existence of a constant c>0 such that the expected fraction of monochrome edges after the FSP is at least 1/2+c. (2) For Erdős–Rényi graphs we show that large common neighborhoods are unlikely and that the expected fraction of monochrome edges after the FSP is at most 1/2+o(1). Our results indicate that the cluster structure of the underlying graph has a significant impact on the obtained segregation strength.}, author = {Bläsius, Thomas and Friedrich, Tobias and Krejca, Martin S. and Molitor, Louise}, journal = {Computational Geometry (CGTA)}, keywords = {sys:relevantfor:ae thomasblaesius louisemolitor martinskrejca tobiasfriedrich year2023 cgta}, pages = 101902, title = {The Impact of Geometry on Monochrome Regions in the Flip Schelling Process}, volume = 108, year = 2023 }

Friedrich, Tobias; Göbel, Andreas; Krejca, Martin S.; Pappik, Marcus Polymer Dynamics via Cliques: New Conditions for ApproximationsTheoretical Computer Science 2023
[ Abstract ] [ BibTeX ] [ Download ]
 
Abstract polymer models are systems of weighted objects, called polymers, equipped with an incompatibility relation. An important quantity associated with such models is the partition function, which is the weighted sum over all sets of compatible polymers. Various approximation problems reduce to approximating the partition function of a polymer model. Central to the existence of such approximation algorithms are weight conditions of the respective polymer model. Such conditions are derived either via complex analysis or via probabilistic arguments. We follow the latter path and establish a new condition—the clique dynamics condition—, which is less restrictive than the ones in the literature. We introduce a new Markov chain where the clique dynamics condition implies rapid mixing by utilizing cliques of incompatible polymers that naturally arise from the translation of algorithmic problems into polymer models. This leads to improved parameter ranges for several approximation algorithms, such as a factor of at least \(2^{1/\alpha}\) for the hard-core model on bipartite \(\alpha\)-expanders.
@article{friedrich2023polymer, abstract = {Abstract polymer models are systems of weighted objects, called polymers, equipped with an incompatibility relation. An important quantity associated with such models is the partition function, which is the weighted sum over all sets of compatible polymers. Various approximation problems reduce to approximating the partition function of a polymer model. Central to the existence of such approximation algorithms are weight conditions of the respective polymer model. Such conditions are derived either via complex analysis or via probabilistic arguments. We follow the latter path and establish a new condition—the clique dynamics condition—, which is less restrictive than the ones in the literature. We introduce a new Markov chain where the clique dynamics condition implies rapid mixing by utilizing cliques of incompatible polymers that naturally arise from the translation of algorithmic problems into polymer models. This leads to improved parameter ranges for several approximation algorithms, such as a factor of at least \(2^{1/\alpha}\) for the hard-core model on bipartite \(\alpha\)-expanders.}, author = {Friedrich, Tobias and Göbel, Andreas and Krejca, Martin S. and Pappik, Marcus}, journal = {Theoretical Computer Science}, keywords = {tcs marcuspappik martinskrejca andreasgoebel tobiasfriedrich year2023}, title = {Polymer Dynamics via Cliques: New Conditions for Approximations}, year = 2023 }

Krogmann, Simon; Lenzner, Pascal; Skopalik, Alexander Strategic Facility Location with Clients that Minimize Total Waiting TimeConference on Artificial Intelligence (AAAI) 2023
[ Abstract ] [ BibTeX ]
 
We study a non-cooperative two-sided facility location game in which facilities and clients behave strategically. This is in contrast to many other facility location games in which clients simply visit their closest facility. Facility agents select a location on a graph to open a facility to attract as much purchasing power as possible, while client agents choose which facilities to patronize by strategically distributing their purchasing power in order to minimize their total waiting time. Here, the waiting time of a facility depends on its received total purchasing power. We show that our client stage is an atomic splittable congestion game, which implies existence, uniqueness and efficient computation of a client equilibrium. Therefore, facility agents can efficiently predict client behavior and make strategic decisions accordingly. Despite that, we prove that subgame perfect equilibria do not exist in all instances of this game and that their existence is NP-hard to decide. On the positive side, we provide a simple and efficient algorithm to compute 3-approximate subgame perfect equilibria.
@inproceedings{krogmann2023strategic, abstract = {We study a non-cooperative two-sided facility location game in which facilities and clients behave strategically. This is in contrast to many other facility location games in which clients simply visit their closest facility. Facility agents select a location on a graph to open a facility to attract as much purchasing power as possible, while client agents choose which facilities to patronize by strategically distributing their purchasing power in order to minimize their total waiting time. Here, the waiting time of a facility depends on its received total purchasing power. We show that our client stage is an atomic splittable congestion game, which implies existence, uniqueness and efficient computation of a client equilibrium. Therefore, facility agents can efficiently predict client behavior and make strategic decisions accordingly. Despite that, we prove that subgame perfect equilibria do not exist in all instances of this game and that their existence is NP-hard to decide. On the positive side, we provide a simple and efficient algorithm to compute 3-approximate subgame perfect equilibria.}, author = {Krogmann, Simon and Lenzner, Pascal and Skopalik, Alexander}, booktitle = {Conference on Artificial Intelligence (AAAI)}, keywords = {aaai year2023 simonkrogmann pascallenzner}, title = {Strategic Facility Location with Clients that Minimize Total Waiting Time}, year = 2023 }

Böther, Maximilian; Kißig, Otto; Weyand, Christopher Efficiently Computing Directed Minimum Spanning TreesSIAM Symposium on Algorithm Engineering and Experiments (ALENEX) 2023
[ Abstract ] [ BibTeX ]
 
Computing a directed minimum spanning tree, called arborescence, is a fundamental algorithmic problem, although not as common as its undirected counterpart. In 1967, Edmonds discussed an elegant solution. It was refined to run in O(min(n2, m log n)) by Tarjan which is optimal for very dense and very sparse graphs. Gabow et al. gave a version of Edmonds’ algorithm that runs in O(n log n +m), thus asymptotically beating the Tarjan variant in the regime between sparse and dense. Despite the attention the problem received theoretically, there exists, to the best of our knowledge, no empirical evaluation of either of these algorithms. In fact, the version by Gabow et al. has never been implemented and, aside from coding competitions, all readily available Tarjan implementations run in O(n2). In this paper, we provide the first implementation of the version by Gabow et al. as well as five variants of Tarjan’s version with different underlying data structures. We evaluate these algorithms and existing solvers on a large set of real-world and random graphs.
@inproceedings{bother2023efficiently, abstract = {Computing a directed minimum spanning tree, called arborescence, is a fundamental algorithmic problem, although not as common as its undirected counterpart. In 1967, Edmonds discussed an elegant solution. It was refined to run in O(min(n2, m log n)) by Tarjan which is optimal for very dense and very sparse graphs. Gabow et al. gave a version of Edmonds’ algorithm that runs in O(n log n +m), thus asymptotically beating the Tarjan variant in the regime between sparse and dense. Despite the attention the problem received theoretically, there exists, to the best of our knowledge, no empirical evaluation of either of these algorithms. In fact, the version by Gabow et al. has never been implemented and, aside from coding competitions, all readily available Tarjan implementations run in O(n2). In this paper, we provide the first implementation of the version by Gabow et al. as well as five variants of Tarjan’s version with different underlying data structures. We evaluate these algorithms and existing solvers on a large set of real-world and random graphs.}, author = {Böther, Maximilian and Kißig, Otto and Weyand, Christopher}, booktitle = {SIAM Symposium on Algorithm Engineering and Experiments (ALENEX)}, keywords = {maximilianboether alenex ottokissig sys:relevantfor:ae christopherweyand year2023}, title = {Efficiently Computing Directed Minimum Spanning Trees}, year = 2023 }

Casel, Katrin; Dierking, Jessica; Dunker, Rebekka; Egbert, Julian; Fischbeck, Philipp; Friedrich, Tobias; Helms, Christian; Isaac, Davis; Khomutovskiy, Ivan; Krogmann, Simon; Lenzner, Pascal; Schöllkopf, Finn Applying Skeletons to Speed Up the Arc-Flags Routing AlgorithmSIAM Symposium on Algorithm Engineering and Experiments (ALENEX) 2023
[ Abstract ] [ BibTeX ]
 
The Single-Source Shortest Path problem is classically solved by applying Dijkstra's algorithm. However, the plain version of this algorithm is far too slow for real-world applications such as routing in large road networks. To amend this, many speed-up techniques have been developed that build on the idea of computing auxiliary data in a preprocessing phase, that is used to speed up the queries. One well-known example is the Arc-Flags algorithm that is based on the idea of precomputing edge flags to make the search more goal-directed. To explain the strong practical performance of such speed-up techniques, several graph parameters have been introduced. The skeleton dimension is one such parameter that has already been used to derive runtime bounds for some speed-up techniques. Moreover, it was experimentally shown to be low in real-world road networks. We introduce a method to incorporate skeletons, the underlying structure behind the skeleton dimension, to improve routing speed-up techniques even further. As a proof of concept, we develop new algorithms called SKARF and SKARF+ that combine skeletons with Arc-Flags, and demonstrate via extensive experiments on large real-world road networks that SKARF+ yields a significant reduction of the search space and the query time of about 30% to 40% over Arc-Flags. We also prove theoretical bounds on the query time of SKARF, which is the first time an Arc-Flags variant has been analyzed in terms of skeleton dimension.
@inproceedings{casel2023applying, abstract = {The Single-Source Shortest Path problem is classically solved by applying Dijkstra's algorithm. However, the plain version of this algorithm is far too slow for real-world applications such as routing in large road networks. To amend this, many speed-up techniques have been developed that build on the idea of computing auxiliary data in a preprocessing phase, that is used to speed up the queries. One well-known example is the Arc-Flags algorithm that is based on the idea of precomputing edge flags to make the search more goal-directed. To explain the strong practical performance of such speed-up techniques, several graph parameters have been introduced. The skeleton dimension is one such parameter that has already been used to derive runtime bounds for some speed-up techniques. Moreover, it was experimentally shown to be low in real-world road networks. We introduce a method to incorporate skeletons, the underlying structure behind the skeleton dimension, to improve routing speed-up techniques even further. As a proof of concept, we develop new algorithms called SKARF and SKARF+ that combine skeletons with Arc-Flags, and demonstrate via extensive experiments on large real-world road networks that SKARF+ yields a significant reduction of the search space and the query time of about 30\% to 40\% over Arc-Flags. We also prove theoretical bounds on the query time of SKARF, which is the first time an Arc-Flags variant has been analyzed in terms of skeleton dimension.}, author = {Casel, Katrin and Dierking, Jessica and Dunker, Rebekka and Egbert, Julian and Fischbeck, Philipp and Friedrich, Tobias and Helms, Christian and Isaac, Davis and Khomutovskiy, Ivan and Krogmann, Simon and Lenzner, Pascal and Schöllkopf, Finn}, booktitle = {SIAM Symposium on Algorithm Engineering and Experiments (ALENEX)}, keywords = {alenex philippfischbeck katrincasel davisissac tobiasfriedrich year2023 simonkrogmann pascallenzner}, title = {Applying Skeletons to Speed Up the Arc-Flags Routing Algorithm}, year = 2023 }

2022

Hacker, Philipp; Naumann, Felix; Friedrich, Tobias; Grundmann, Stefan; Lehmann, Anja AI Compliance - Challenges of Bridging Data Science and LawACM Journal of Data and Information Quality 2022
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
This vision paper outlines the main building blocks of what we term AI Compliance, an effort to bridge two complementary research areas: computer science and the law. Such research has the goal to model, measure, and affect the quality of AI artifacts, such as data, models and applications, to then facilitate adherence to legal standards.
@article{hacker2022compliance, abstract = {This vision paper outlines the main building blocks of what we term AI Compliance, an effort to bridge two complementary research areas: computer science and the law. Such research has the goal to model, measure, and affect the quality of AI artifacts, such as data, models and applications, to then facilitate adherence to legal standards.}, author = {Hacker, Philipp and Naumann, Felix and Friedrich, Tobias and Grundmann, Stefan and Lehmann, Anja}, journal = {ACM Journal of Data and Information Quality}, keywords = {myown tobiasfriedrich}, title = {AI Compliance - Challenges of Bridging Data Science and Law}, year = 2022 }

Bläsius, Thomas; Freiberger, Cedric; Friedrich, Tobias; Katzmann, Maximilian; Montenegro-Retana, Felix; Thieffry, Marianne Efficient Shortest Paths in Scale-Free Networks with Underlying Hyperbolic GeometryACM Transactions on Algorithms 2022: 1–32
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
A standard approach to accelerating shortest path algorithms on networks is the bidirectional search, which explores the graph from the start and the destination, simultaneously. In practice this strategy performs particularly well on scale-free real-world networks. Such networks typically have a heterogeneous degree distribution (e.g., a power-law distribution) and high clustering (i.e., vertices with a common neighbor are likely to be connected themselves). These two properties can be obtained by assuming an underlying hyperbolic geometry. To explain the observed behavior of the bidirectional search, we analyze its running time on hyperbolic random graphs and prove that it is \(\tilde{O}(n\)\(^{2 - 1/ \alpha}+\)\(n^{1/(2\alpha)}\)\(+ \delta_{\max})\) with high probability, where \(\alpha\)\(\in\)\((0.5, 1)\) controls the power-law exponent of the degree distribution, and \(\delta_{\max}\) is the maximum degree. This bound is sublinear, improving the obvious worst-case linear bound. Although our analysis depends on the underlying geometry, the algorithm itself is oblivious to it.
@article{blasius2022efficient, abstract = {A standard approach to accelerating shortest path algorithms on networks is the bidirectional search, which explores the graph from the start and the destination, simultaneously. In practice this strategy performs particularly well on scale-free real-world networks. Such networks typically have a heterogeneous degree distribution (e.g., a power-law distribution) and high clustering (i.e., vertices with a common neighbor are likely to be connected themselves). These two properties can be obtained by assuming an underlying hyperbolic geometry. To explain the observed behavior of the bidirectional search, we analyze its running time on hyperbolic random graphs and prove that it is \(\tilde{O}(n\)\(^{2 - 1/ \alpha}+\)\(n^{1/(2\alpha)}\)\(+ \delta_{\max})\) with high probability, where \(\alpha\)\(\in\)\((0.5, 1)\) controls the power-law exponent of the degree distribution, and \(\delta_{\max}\) is the maximum degree. This bound is sublinear, improving the obvious worst-case linear bound. Although our analysis depends on the underlying geometry, the algorithm itself is oblivious to it.}, author = {Bläsius, Thomas and Freiberger, Cedric and Friedrich, Tobias and Katzmann, Maximilian and Montenegro-Retana, Felix and Thieffry, Marianne}, journal = {ACM Transactions on Algorithms}, keywords = {sys:relevantfor:ae thomasblaesius tobiasfriedrich mariannethieffry cedricfreiberger maximiliankatzmann year2022 felixmontenegroretana}, pages = {1-32}, title = {Efficient Shortest Paths in Scale-Free Networks with Underlying Hyperbolic Geometry}, year = 2022 }

Bilò, Davide; Bilò, Vittorio; Lenzner, Pascal; Molitor, Louise Topological Influence and Locality in Swap Schelling GamesAutonomous Agents and Multi-Agent Systems (AGNT) 2022: 47
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Residential segregation is a wide-spread phenomenon that can be observed in almost every major city. In these urban areas residents with different racial or socioeconomic background tend to form homogeneous clusters. Schelling's famous agent-based model for residential segregation explains how such clusters can form even if all agents are tolerant, i.e., if they agree to live in mixed neighborhoods. For segregation to occur, all it needs is a slight bias towards agents preferring similar neighbors. Very recently, Schelling's model has been investigated from a game-theoretic point of view with selfish agents that strategically select their residential location. In these games, agents can improve on their current location by performing a location swap with another agent who is willing to swap. We significantly deepen these investigations by studying the influence of the underlying topology modeling the residential area on the existence of equilibria, the Price of Anarchy and on the dynamic properties of the resulting strategic multi-agent system. Moreover, as a new conceptual contribution, we also consider the influence of locality, i.e., if the location swaps are restricted to swaps of neighboring agents. We give improved almost tight bounds on the Price of Anarchy for arbitrary underlying graphs and we present (almost) tight bounds for regular graphs, paths and cycles. Moreover, we give almost tight bounds for grids, which are commonly used in empirical studies. For grids we also show that locality has a severe impact on the game dynamics.
@article{bilo2022topological, abstract = {Residential segregation is a wide-spread phenomenon that can be observed in almost every major city. In these urban areas residents with different racial or socioeconomic background tend to form homogeneous clusters. Schelling's famous agent-based model for residential segregation explains how such clusters can form even if all agents are tolerant, i.e., if they agree to live in mixed neighborhoods. For segregation to occur, all it needs is a slight bias towards agents preferring similar neighbors. Very recently, Schelling's model has been investigated from a game-theoretic point of view with selfish agents that strategically select their residential location. In these games, agents can improve on their current location by performing a location swap with another agent who is willing to swap. We significantly deepen these investigations by studying the influence of the underlying topology modeling the residential area on the existence of equilibria, the Price of Anarchy and on the dynamic properties of the resulting strategic multi-agent system. Moreover, as a new conceptual contribution, we also consider the influence of locality, i.e., if the location swaps are restricted to swaps of neighboring agents. We give improved almost tight bounds on the Price of Anarchy for arbitrary underlying graphs and we present (almost) tight bounds for regular graphs, paths and cycles. Moreover, we give almost tight bounds for grids, which are commonly used in empirical studies. For grids we also show that locality has a severe impact on the game dynamics.}, author = {Bilò, Davide and Bilò, Vittorio and Lenzner, Pascal and Molitor, Louise}, journal = {Autonomous Agents and Multi-Agent Systems (AGNT)}, keywords = {louisemolitor agnt year2022 pascallenzner}, number = 2, pages = 47, title = {Topological Influence and Locality in Swap Schelling Games}, volume = 36, year = 2022 }

Casel, Katrin; Fischbeck, Philipp; Friedrich, Tobias; Göbel, Andreas; Lagodzinski, J. A. Gregor Zeros and approximations of Holant polynomials on the complex planeComputational Complexity 2022: 11
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
We present fully polynomial time approximation schemesfor a broad class of Holant problems with complex edge weights, which we call Holant polynomials. We transform these problems into partition functions of abstract combinatorial structures known as polymers in statistical physics. Our method involves establishing zero-free regions for the partition functions of polymer models and using the mostsignificant terms of the cluster expansion to approximate them. Results of our technique include new approximation and sampling algorithms for a diverse class of Holant polynomials in the low-temperature regime (i.e. small external field) and approximation algorithms for general Holant problems with small signature weights. Additionally, we give randomised approximation and sampling algorithms with faster running times for more restrictive classes. Finally, we improve the known zero-free regions for a perfect matching polynomial.
@article{casel2022zeros, abstract = {We present fully polynomial time approximation schemesfor a broad class of Holant problems with complex edge weights, which we call Holant polynomials. We transform these problems into partition functions of abstract combinatorial structures known as polymers in statistical physics. Our method involves establishing zero-free regions for the partition functions of polymer models and using the mostsignificant terms of the cluster expansion to approximate them. Results of our technique include new approximation and sampling algorithms for a diverse class of Holant polynomials in the low-temperature regime (i.e. small external field) and approximation algorithms for general Holant problems with small signature weights. Additionally, we give randomised approximation and sampling algorithms with faster running times for more restrictive classes. Finally, we improve the known zero-free regions for a perfect matching polynomial.}, author = {Casel, Katrin and Fischbeck, Philipp and Friedrich, Tobias and Göbel, Andreas and Lagodzinski, J. A. Gregor}, journal = {Computational Complexity}, keywords = {gregorlagodzinski philippfischbeck katrincasel andreasgoebel tobiasfriedrich year2022 cc}, number = 2, pages = 11, title = {Zeros and approximations of Holant polynomials on the complex plane}, volume = 31, year = 2022 }

Casel, Katrin; Fernau, Henning; Grigoriev, Alexander; Schmid, Markus L.; Whitesides, Sue Combinatorial Properties and Recognition of Unit Square Visibility GraphsDiscrete & Computational Geometry 2022
[ Abstract ] [ BibTeX ] [ Download ]
 
Unit square visibility graphs (USV) are described by axis-parallel visibility between unit squares placed in the plane. If the squares are required to be placed on integer grid coordinates, then USV become unit square grid visibility graphs (USGV), an alternative characterisation of the well-known rectilinear graphs. We extend known combinatorial results for USGV and we show that, in the weak case (i.e., visibilities do not necessarily translate into edges of the represented combinatorial graph), the area minimisation variant of their recognition problem is NP-hard. We also provide combinatorial insights with respect to USV, and as our main result, we prove their recognition problem to be \($\mathcal{NP}$\)-hard, which settles an open question.
@article{casel2022combinatorial, abstract = {Unit square visibility graphs (USV) are described by axis-parallel visibility between unit squares placed in the plane. If the squares are required to be placed on integer grid coordinates, then USV become unit square grid visibility graphs (USGV), an alternative characterisation of the well-known rectilinear graphs. We extend known combinatorial results for USGV and we show that, in the weak case (i.e., visibilities do not necessarily translate into edges of the represented combinatorial graph), the area minimisation variant of their recognition problem is NP-hard. We also provide combinatorial insights with respect to USV, and as our main result, we prove their recognition problem to be $\mathcal{NP}$-hard, which settles an open question.}, author = {Casel, Katrin and Fernau, Henning and Grigoriev, Alexander and Schmid, Markus L. and Whitesides, Sue}, journal = {Discrete \& Computational Geometry}, keywords = {katrincasel dcg year2022}, title = {Combinatorial Properties and Recognition of Unit Square Visibility Graphs}, year = 2022 }

Bläsius, Thomas; Friedrich, Tobias; Lischeid, Julius; Meeks, Kitty; Schirneck, Martin Efficiently Enumerating Hitting Sets of Hypergraphs Arising in Data ProfilingJournal of Computer and System Sciences 2022: 192–213
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
The transversal hypergraph problem asks to enumerate the minimal hitting sets of a hypergraph. If the solutions have bounded size, Eiter and Gottlob [SICOMP’95] gave an algorithm running in output-polynomial time, but whose space requirement also scales with the output. We improve this to polynomial delay and space. Central to our approach is the extension problem, deciding for a set X of vertices whether it is contained in any minimal hitting set. We show that this is one of the first natural problems to be W[3]-complete. We give an algorithm for the extension problem running in time O(m |X|+1 n) and prove a SETH-lower bound showing that this is close to optimal. We apply our enumeration method to the discovery problem of minimal unique column combinations from data profiling. Our empirical evaluation suggests that the algorithm outperforms its worst-case guarantees on hypergraphs stemming from real-world databases.
@article{Blaesius22Efficiently, abstract = {The transversal hypergraph problem asks to enumerate the minimal hitting sets of a hypergraph. If the solutions have bounded size, Eiter and Gottlob [SICOMP’95] gave an algorithm running in output-polynomial time, but whose space requirement also scales with the output. We improve this to polynomial delay and space. Central to our approach is the extension problem, deciding for a set X of vertices whether it is contained in any minimal hitting set. We show that this is one of the first natural problems to be W[3]-complete. We give an algorithm for the extension problem running in time O(m |X|+1 n) and prove a SETH-lower bound showing that this is close to optimal. We apply our enumeration method to the discovery problem of minimal unique column combinations from data profiling. Our empirical evaluation suggests that the algorithm outperforms its worst-case guarantees on hypergraphs stemming from real-world databases.}, author = {Bläsius, Thomas and Friedrich, Tobias and Lischeid, Julius and Meeks, Kitty and Schirneck, Martin}, journal = {Journal of Computer and System Sciences}, keywords = {kittymeeks thomasblaesius juliuslischeid tobiasfriedrich year2022 martinschirneck}, pages = {192-213}, title = {Efficiently Enumerating Hitting Sets of Hypergraphs Arising in Data Profiling}, volume = 124, year = 2022 }

Friedrich, Tobias; Göbel, Andreas; Krejca, Martin S.; Pappik, Marcus A Spectral Independence View on Hard Spheres via Block DynamicsSIAM Journal on Discrete Mathematics 2022: 2282–2322
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The hard-sphere model is one of the most extensively studied models in statistical physics. It describes the continuous distribution of spherical particles, governed by hard-core interactions. An important quantity of this model is the normalizing factor of this distribution, called the partition function. We propose a Markov chain Monte Carlo algorithm for approximating the grand canonical partition function of the hard-sphere model in \(d\) dimensions. Up to a fugacity of \(\lambda < \mathrm{e / 2d\), the runtime of our algorithm is polynomial in the volume of the system. Key to our approach is to define a discretization that closely approximates the partition function of the continuous model. This results in a discrete hard-core instance that is exponential in the size of the initial hard-sphere model. Our approximation bound follows directly from the correlation decay threshold of an infinite regular tree with degree equal to the maximum degree of our discretization. To cope with the exponential blow-up of the discrete instance, we use block dynamics, a Markov chain that generalizes the more frequently studied Glauber dynamics by grouping the vertices of the graph into blocks and updating an entire block instead of a single vertex in each step. We prove rapid mixing of block dynamics, based on disjoint cliques as blocks, up to the tree threshold of the univariate hard-core model. This is achieved by adapting the spectral expansion method, which was recently used for bounding the mixing time of Glauber dynamics within the same parameter regime.
@article{friedrich2022spectral, abstract = {The hard-sphere model is one of the most extensively studied models in statistical physics. It describes the continuous distribution of spherical particles, governed by hard-core interactions. An important quantity of this model is the normalizing factor of this distribution, called the partition function. We propose a Markov chain Monte Carlo algorithm for approximating the grand canonical partition function of the hard-sphere model in \(d\) dimensions. Up to a fugacity of \(\lambda < \mathrm{e} / 2d\), the runtime of our algorithm is polynomial in the volume of the system. Key to our approach is to define a discretization that closely approximates the partition function of the continuous model. This results in a discrete hard-core instance that is exponential in the size of the initial hard-sphere model. Our approximation bound follows directly from the correlation decay threshold of an infinite regular tree with degree equal to the maximum degree of our discretization. To cope with the exponential blow-up of the discrete instance, we use block dynamics, a Markov chain that generalizes the more frequently studied Glauber dynamics by grouping the vertices of the graph into blocks and updating an entire block instead of a single vertex in each step. We prove rapid mixing of block dynamics, based on disjoint cliques as blocks, up to the tree threshold of the univariate hard-core model. This is achieved by adapting the spectral expansion method, which was recently used for bounding the mixing time of Glauber dynamics within the same parameter regime.}, author = {Friedrich, Tobias and Göbel, Andreas and Krejca, Martin S. and Pappik, Marcus}, journal = {SIAM Journal on Discrete Mathematics}, keywords = {marcuspappik martinskrejca andreasgoebel tobiasfriedrich year2022}, number = 3, pages = {2282-2322}, title = {A Spectral Independence View on Hard Spheres via Block Dynamics}, volume = 36, year = 2022 }

Bläsius, Thomas; Friedrich, Tobias; Schirneck, Martin The Complexity of Dependency Detection and Discovery in Relational DatabasesTheoretical Computer Science 2022: 79–96
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Multi-column dependencies in relational databases come associated with two different computational tasks. The detection problem is to decide whether a dependency of a certain type and size holds in a given database, the discovery problem asks to enumerate all valid dependencies of that type. We settle the complexity of both of these problems for unique column combinations (UCCs), functional dependencies (FDs), and inclusion dependencies (INDs). We show that the detection of UCCs and FDs is W[2]-complete when parameterized by the solution size. The discovery of inclusion-wise minimal UCCs is proven to be equivalent under parsimonious reductions to the transversal hypergraph problem of enumerating the minimal hitting sets of a hypergraph. The discovery of FDs is equivalent to the simultaneous enumeration of the hitting sets of multiple input hypergraphs. We further identify the detection of INDs as one of the first natural W[3]-complete problems. The discovery of maximal INDs is shown to be equivalent to enumerating the maximal satisfying assignments of antimonotone, 3-normalized Boolean formulas.
@article{blaesius2022complexity, abstract = {Multi-column dependencies in relational databases come associated with two different computational tasks. The detection problem is to decide whether a dependency of a certain type and size holds in a given database, the discovery problem asks to enumerate all valid dependencies of that type. We settle the complexity of both of these problems for unique column combinations (UCCs), functional dependencies (FDs), and inclusion dependencies (INDs). We show that the detection of UCCs and FDs is W[2]-complete when parameterized by the solution size. The discovery of inclusion-wise minimal UCCs is proven to be equivalent under parsimonious reductions to the transversal hypergraph problem of enumerating the minimal hitting sets of a hypergraph. The discovery of FDs is equivalent to the simultaneous enumeration of the hitting sets of multiple input hypergraphs. We further identify the detection of INDs as one of the first natural W[3]-complete problems. The discovery of maximal INDs is shown to be equivalent to enumerating the maximal satisfying assignments of antimonotone, 3-normalized Boolean formulas.}, author = {Bläsius, Thomas and Friedrich, Tobias and Schirneck, Martin}, journal = {Theoretical Computer Science}, keywords = {tcs thomasblaesius tobiasfriedrich year2022 martinschirneck}, pages = {79-96}, title = {The Complexity of Dependency Detection and Discovery in Relational Databases}, volume = 900, year = 2022 }

Bandyapadhyay, Sayan; Fomin, Fedor V.; Golovach, Petr A.; Lochet, William; Purohit, Nidhi; Simonov, Kirill How to Find a Good Explanation for Clustering?Conference on Artificial Intelligence (AAAI) 2022: 3904–3912
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
\(k\)-means and \(k\)-median clustering are powerful unsupervised machine learning techniques. However, due to complicated dependences on all the features, it is challenging to interpret the resulting cluster assignments. Moshkovitz, Dasgupta, Rashtchian, and Frost proposed an elegant model of explainable \(k\)-means and \(k\)-median clustering in ICML 2020. In this model, a decision tree with \(k\) leaves provides a straightforward characterization of the data set into clusters. We study two natural algorithmic questions about explainable clustering. (1) For a given clustering, how to find the ``best explanation'' by using a decision tree with \(k\) leaves? (2) For a given set of points, how to find a decision tree with \(k\) leaves minimizing the \(k\)-means/median objective of the resulting explainable clustering? To address the first question, we introduce a new model of explainable clustering. Our model, inspired by the notion of outliers in robust statistics, is the following. We are seeking a small number of points (outliers) whose removal makes the existing clustering well-explainable. For addressing the second question, we initiate the study of the model of Moshkovitz et al. from the perspective of multivariate complexity. Our rigorous algorithmic analysis sheds some light on the influence of parameters like the input size, dimension of the data, the number of outliers, the number of clusters, and the approximation ratio, on the computational complexity of explainable clustering.
@inproceedings{bandyapadhyay2022explanation, abstract = {\(k\)-means and \(k\)-median clustering are powerful unsupervised machine learning techniques. However, due to complicated dependences on all the features, it is challenging to interpret the resulting cluster assignments. Moshkovitz, Dasgupta, Rashtchian, and Frost proposed an elegant model of explainable \(k\)-means and \(k\)-median clustering in ICML 2020. In this model, a decision tree with \(k\) leaves provides a straightforward characterization of the data set into clusters. We study two natural algorithmic questions about explainable clustering. (1) For a given clustering, how to find the ``best explanation'' by using a decision tree with \(k\) leaves? (2) For a given set of points, how to find a decision tree with \(k\) leaves minimizing the \(k\)-means/median objective of the resulting explainable clustering? To address the first question, we introduce a new model of explainable clustering. Our model, inspired by the notion of outliers in robust statistics, is the following. We are seeking a small number of points (outliers) whose removal makes the existing clustering well-explainable. For addressing the second question, we initiate the study of the model of Moshkovitz et al. from the perspective of multivariate complexity. Our rigorous algorithmic analysis sheds some light on the influence of parameters like the input size, dimension of the data, the number of outliers, the number of clusters, and the approximation ratio, on the computational complexity of explainable clustering.}, author = {Bandyapadhyay, Sayan and Fomin, Fedor V. and Golovach, Petr A. and Lochet, William and Purohit, Nidhi and Simonov, Kirill}, booktitle = {Conference on Artificial Intelligence (AAAI)}, keywords = {sys:relevantfor:ae kirillsimonov aaai year2022}, pages = {3904-3912}, title = {How to Find a Good Explanation for Clustering?}, year = 2022 }

Cseh, Ágnes; Peters, Jannik Three-Dimensional Popular Matching with Cyclic PreferencesAutonomous Agents and Multi-Agent Systems (AAMAS) 2022: 77–87
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Two actively researched problem settings in matchings under preferences are popular matchings and the three-dimensional stable matching problem with cyclic preferences. In this paper, we apply the optimality notion of the first topic to the input characteristics of the second one. We investigate the connection between stability, popularity, and their strict variants, strong stability and strong popularity in three-dimensional instances with cyclic preferences. Furthermore, we also derive results on the complexity of these problems when the preferences are derived from master lists.
@inproceedings{cseh2022threedimensional, abstract = {Two actively researched problem settings in matchings under preferences are popular matchings and the three-dimensional stable matching problem with cyclic preferences. In this paper, we apply the optimality notion of the first topic to the input characteristics of the second one. We investigate the connection between stability, popularity, and their strict variants, strong stability and strong popularity in three-dimensional instances with cyclic preferences. Furthermore, we also derive results on the complexity of these problems when the preferences are derived from master lists.}, author = {Cseh, Ágnes and Peters, Jannik}, booktitle = {Autonomous Agents and Multi-Agent Systems (AAMAS)}, keywords = {jannikpeters agnescseh aamas year2022}, pages = {77&ndash;87}, title = {Three-Dimensional Popular Matching with Cyclic Preferences}, year = 2022 }

Berenbrink, Petra; Hoefer, Martin; Kaaser, Dominik; Lenzner, Pascal; Rau, Malin; Schmand, Daniel Asynchronous Opinion Dynamics in Social NetworksAutonomous Agents and Multi-Agent Systems (AAMAS) 2022: 109–117
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Opinion spreading in a society decides the fate of elections, the success of products, and the impact of political or social movements. The model by Hegselmann and Krause is a well-known theoretical model to study such opinion formation processes in social networks. In contrast to many other theoretical models, it does not converge towards a situation where all agents agree on the same opinion. Instead, it assumes that people find an opinion reasonable if and only if it is close to their own. The system converges towards a stable situation where agents sharing the same opinion form a cluster, and agents in different clusters do not influence each other. We focus on the social variant of the Hegselmann-Krause model where agents are connected by a social network and their opinions evolve in an iterative process. When activated, an agent adopts the average of the opinions of its neighbors having a similar opinion. By this, the set of influencing neighbors of an agent may change over time. To the best of our knowledge, social Hegselmann-Krause systems with asynchronous opinion updates have only been studied with the complete graph as social network. We show that such opinion dynamics with random agent activation are guaranteed to converge for any social network. We provide an upper bound of \(\mathcal{O(n |E|^2 (\varepsilon/\delta)^2)\) on the expected number of opinion updates until convergence, where |E| is the number of edges of the social network. For the complete social network we show a bound of \( \mathcal{O(n^3(n^2 + (\varepsilon/\delta)^2)) \) that represents a major improvement over the previously best upper bound of \( \mathcal{O(n^9(\varepsilon/\delta)^2) \). Our bounds are complemented by simulations that indicate asymptotically matching lower bounds.
@inproceedings{berenbrink2022asynchronous, abstract = {Opinion spreading in a society decides the fate of elections, the success of products, and the impact of political or social movements. The model by Hegselmann and Krause is a well-known theoretical model to study such opinion formation processes in social networks. In contrast to many other theoretical models, it does not converge towards a situation where all agents agree on the same opinion. Instead, it assumes that people find an opinion reasonable if and only if it is close to their own. The system converges towards a stable situation where agents sharing the same opinion form a cluster, and agents in different clusters do not influence each other. We focus on the social variant of the Hegselmann-Krause model where agents are connected by a social network and their opinions evolve in an iterative process. When activated, an agent adopts the average of the opinions of its neighbors having a similar opinion. By this, the set of influencing neighbors of an agent may change over time. To the best of our knowledge, social Hegselmann-Krause systems with asynchronous opinion updates have only been studied with the complete graph as social network. We show that such opinion dynamics with random agent activation are guaranteed to converge for any social network. We provide an upper bound of \(\mathcal{O}(n |E|^2 (\varepsilon/\delta)^2)\) on the expected number of opinion updates until convergence, where |E| is the number of edges of the social network. For the complete social network we show a bound of \( \mathcal{O}(n^3(n^2 + (\varepsilon/\delta)^2)) \) that represents a major improvement over the previously best upper bound of \( \mathcal{O}(n^9(\varepsilon/\delta)^2) \). Our bounds are complemented by simulations that indicate asymptotically matching lower bounds.}, author = {Berenbrink, Petra and Hoefer, Martin and Kaaser, Dominik and Lenzner, Pascal and Rau, Malin and Schmand, Daniel}, booktitle = {Autonomous Agents and Multi-Agent Systems (AAMAS)}, keywords = {aamas year2022 pascallenzner}, pages = {109&ndash;117}, title = {Asynchronous Opinion Dynamics in Social Networks}, year = 2022 }

Cseh, Ágnes; Friedrich, Tobias; Peters, Jannik Pareto Optimal and Popular House Allocation with Lower and Upper QuotasAutonomous Agents and Multi-Agent Systems (AAMAS) 2022: 300–308
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
In the house allocation problem with lower and upper quotas, we are given a set of applicants and a set of projects. Each applicant has a strictly ordered preference list over the projects, while the projects are equipped with a lower and an upper quota. A feasible matching assigns the applicants to the projects in such a way that a project is either matched to no applicant or to a number of applicants between its lower and upper quota. In this model we study two classic optimality concepts: Pareto optimality and popularity. We show that finding a popular matching is hard even if the maximum lower quota is 2 and that finding a perfect Pareto optimal matching, verifying Pareto optimality, and verifying popularity are all NP-complete even if the maximum lower quota is 3. We complement the last three negative results by showing that the problems become polynomial-time solvable when the maximum lower quota is 2, thereby answering two open questions of Cechlárová and Fleiner. Finally, we also study the parameterized complexity of all four mentioned problems.
@inproceedings{cseh2022pareto, abstract = {In the house allocation problem with lower and upper quotas, we are given a set of applicants and a set of projects. Each applicant has a strictly ordered preference list over the projects, while the projects are equipped with a lower and an upper quota. A feasible matching assigns the applicants to the projects in such a way that a project is either matched to no applicant or to a number of applicants between its lower and upper quota. In this model we study two classic optimality concepts: Pareto optimality and popularity. We show that finding a popular matching is hard even if the maximum lower quota is 2 and that finding a perfect Pareto optimal matching, verifying Pareto optimality, and verifying popularity are all NP-complete even if the maximum lower quota is 3. We complement the last three negative results by showing that the problems become polynomial-time solvable when the maximum lower quota is 2, thereby answering two open questions of Cechlárová and Fleiner. Finally, we also study the parameterized complexity of all four mentioned problems.}, author = {Cseh, Ágnes and Friedrich, Tobias and Peters, Jannik}, booktitle = {Autonomous Agents and Multi-Agent Systems (AAMAS)}, keywords = {jannikpeters agnescseh tobiasfriedrich aamas year2022}, pages = {300&ndash;308}, title = {Pareto Optimal and Popular House Allocation with Lower and Upper Quotas}, year = 2022 }

Bläsius, Thomas; Friedrich, Tobias; Stangl, David; Weyand, Christopher An Efficient Branch-and-Bound Solver for Hitting SetAlgorithm Engineering and Experiments (ALENEX) 2022
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
The hitting set problem asks for a collection of sets over a universe \(U\) to find a minimum subset of \(U\) that intersects each of the given sets. It is NP-hard and equivalent to the problem set cover. We give a branch-and-bound algorithm to solve hitting set. Though it requires exponential time in the worst case, it can solve many practical instance from different domains in reasonable time. Our algorithm outperforms a modern ILP solver, the state-of-the-art for hitting set, by at least an order of magnitude on most instances.
@inproceedings{blasius2022efficient, abstract = {The hitting set problem asks for a collection of sets over a universe \(U\) to find a minimum subset of \(U\) that intersects each of the given sets. It is NP-hard and equivalent to the problem set cover. We give a branch-and-bound algorithm to solve hitting set. Though it requires exponential time in the worst case, it can solve many practical instance from different domains in reasonable time. Our algorithm outperforms a modern ILP solver, the state-of-the-art for hitting set, by at least an order of magnitude on most instances.}, author = {Bläsius, Thomas and Friedrich, Tobias and Stangl, David and Weyand, Christopher}, booktitle = {Algorithm Engineering and Experiments (ALENEX)}, keywords = {alenex thomasblaesius tobiasfriedrich christopherweyand davidstangl year2022}, title = {An Efficient Branch-and-Bound Solver for Hitting Set}, year = 2022 }

Friedrich, Tobias; Issac, Davis; Kumar, Nikhil; Mallek, Nadym; Zeif, Ziena A Primal-Dual Algorithm for Multicommodity Flows and Multicuts in Treewidth-2 GraphsApproximation Algorithms for Combinatorial Optimization Problems (APPROX) 2022: 55:1–55:18
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
We study the problem of multicommodity flow and multicut in treewidth-2 graphs and prove bounds on the multiflow-multicut gap. In particular, we give a primal-dual algorithm for computing multicommodity flow and multicut in treewidth-2 graphs and prove the following approximate max-flow min-cut theorem: given a treewidth-2 graph, there exists a multicommodity flow of value \(f\) with congestion \(4\), and a multicut of capacity \(c\) such that \(c \leq 20f \) . This implies a multiflow-multicut gap of \(80\) and improves upon the previous best known bounds for such graphs. Our algorithm runs in polynomial time when all the edges have capacity one. Our algorithm is completely combinatorial and builds upon the primal-dual algorithm of Garg, Vazirani and Yannakakis for multicut in trees and the augmenting paths framework of Ford and Fulkerson.
@inproceedings{friedrich2022primaldual, abstract = {We study the problem of multicommodity flow and multicut in treewidth-2 graphs and prove bounds on the multiflow-multicut gap. In particular, we give a primal-dual algorithm for computing multicommodity flow and multicut in treewidth-2 graphs and prove the following approximate max-flow min-cut theorem: given a treewidth-2 graph, there exists a multicommodity flow of value \(f\) with congestion \(4\), and a multicut of capacity \(c\) such that \(c \leq 20f \) . This implies a multiflow-multicut gap of \(80\) and improves upon the previous best known bounds for such graphs. Our algorithm runs in polynomial time when all the edges have capacity one. Our algorithm is completely combinatorial and builds upon the primal-dual algorithm of Garg, Vazirani and Yannakakis for multicut in trees and the augmenting paths framework of Ford and Fulkerson.}, author = {Friedrich, Tobias and Issac, Davis and Kumar, Nikhil and Mallek, Nadym and Zeif, Ziena}, booktitle = {Approximation Algorithms for Combinatorial Optimization Problems (APPROX)}, keywords = {sys:relevantfor:ae zienazeif nikhilkumar davisissac tobiasfriedrich approx nadymmallek year2022}, pages = {55:1&ndash;55:18}, title = {A Primal-Dual Algorithm for Multicommodity Flows and Multicuts in Treewidth-2 Graphs}, year = 2022 }

Doskoč, Vanja; Kötzing, Timo Maps of Restrictions for Behaviourally Correct LearningComputability in Europe (CiE) 2022: 103–114
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In language learning in the limit, we study computable devices (learners) learning formal languages. We consider learning tasks paired with restrictions regarding, for example, the hypotheses made by the learners. We compare such restrictions with each other in order to study their impact and depict the results in overviews, the so-called maps. In~the case of explanatory learning, the literature already provides various maps. On the other hand, in the case of behaviourally correct learning, only partial results are known. In this work, we complete these results and provide full behaviourally correct maps for different types of data presentation. In particular, in all studied settings, we observe that monotone learning implies non-U-shaped learning and that cautiousness, semantic conservativeness and weak monotonicity are equally powerful.
@inproceedings{doskoc2022restrictions, abstract = {In language learning in the limit, we study computable devices (learners) learning formal languages. We consider learning tasks paired with restrictions regarding, for example, the hypotheses made by the learners. We compare such restrictions with each other in order to study their impact and depict the results in overviews, the so-called maps. In&nbsp;the case of explanatory learning, the literature already provides various maps. On the other hand, in the case of behaviourally correct learning, only partial results are known. In this work, we complete these results and provide full behaviourally correct maps for different types of data presentation. In particular, in all studied settings, we observe that monotone learning implies non-U-shaped learning and that cautiousness, semantic conservativeness and weak monotonicity are equally powerful.}, author = {Doskoč, Vanja and Kötzing, Timo}, booktitle = {Computability in Europe (CiE)}, keywords = {vanjadoskoc timokoetzing year2022 cie}, pages = {103-114}, title = {Maps of Restrictions for Behaviourally Correct Learning}, volume = 13359, year = 2022 }

Friedrich, Tobias; Göbel, Andreas; Katzmann, Maximilian; Krejca, Martin S.; Pappik, Marcus Algorithms for hard-constraint point processes via discretizationInternational Computing and Combinatorics Conference (COCOON) 2022
[ Abstract ] [ BibTeX ] [ Download ]
 
We study the algorithmic applications of a natural discretization for the hard-sphere model and the Widom--Rowlinson model in a region of \(d\)-dimensional Euclidean space \(V \subset \mathbf{R}^{d}\). These continuous models are frequently used in statistical physics to describe mixtures of one or multiple particle types subjected to hard-core interactions. For each type, particles are distributed according to a Poisson point process with a type-specific activity parameter, called fugacity. The Gibbs distribution over all possible system states is characterized by the mixture of these point processes conditioned that no two particles are closer than some type-dependent distance threshold. A key part in better understanding the Gibbs distribution is its normalizing constant, called partition function. Our main algorithmic result is the first deterministic approximation algorithm for the partition function of the hard-sphere model and the Widom--Rowlinson model in box-shaped regions of Euclidean space. Our algorithms have quasi-polynomial running time in the volume of the region \(\nu(V)\) if the fugacity is below a certain threshold. For the \(d\)-dimensional hard-sphere model with particles of unit volume, this threshold is \(\mathrm{e}/2^d\). As the number of dimensions \(d\) increases, this bound asymptotically matches the best known results for randomized approximation of the hard-sphere partition function. We prove similar bounds for the Widom--Rowlinson model. To the best of our knowledge, this is the first rigorous algorithmic result for this model.
@inproceedings{friedrich2022algorithms, abstract = {We study the algorithmic applications of a natural discretization for the hard-sphere model and the Widom&ndash;Rowlinson model in a region of \(d\)-dimensional Euclidean space \(V \subset \mathbf{R}^{d}\). These continuous models are frequently used in statistical physics to describe mixtures of one or multiple particle types subjected to hard-core interactions. For each type, particles are distributed according to a Poisson point process with a type-specific activity parameter, called fugacity. The Gibbs distribution over all possible system states is characterized by the mixture of these point processes conditioned that no two particles are closer than some type-dependent distance threshold. A key part in better understanding the Gibbs distribution is its normalizing constant, called partition function. Our main algorithmic result is the first deterministic approximation algorithm for the partition function of the hard-sphere model and the Widom&ndash;Rowlinson model in box-shaped regions of Euclidean space. Our algorithms have quasi-polynomial running time in the volume of the region \(\nu(V)\) if the fugacity is below a certain threshold. For the \(d\)-dimensional hard-sphere model with particles of unit volume, this threshold is \(\mathrm{e}/2^d\). As the number of dimensions \(d\) increases, this bound asymptotically matches the best known results for randomized approximation of the hard-sphere partition function. We prove similar bounds for the Widom&ndash;Rowlinson model. To the best of our knowledge, this is the first rigorous algorithmic result for this model.}, author = {Friedrich, Tobias and Göbel, Andreas and Katzmann, Maximilian and Krejca, Martin S. and Pappik, Marcus}, booktitle = {International Computing and Combinatorics Conference (COCOON)}, keywords = {marcuspappik martinskrejca andreasgoebel tobiasfriedrich cocoon maximiliankatzmann year2022}, title = {Algorithms for hard-constraint point processes via discretization}, year = 2022 }

Hildebrandt, Philipp; Schulze, Maximilian; Cohen, Sarel; Doskoč, Vanja; Saabni, Raid; Friedrich, Tobias Optical Character Recognition Guided Image Super ResolutionSymposium on Document Engineering (DocEng) 2022: 1–4
[ Abstract ] [ BibTeX ] [ URL ] [ Download ]
 
Recognizing disturbed text in real-life images is a difficult problem, as information that is missing due to low resolution or out-of-focus text has to be recreated. Combining text super-resolution and optical character recognition deep learning models can be a valuable tool to enlarge and enhance text images for better readability, as well as recognize text automatically afterwards. We achieve improved peak signal-to-noise ratio and text recognition accuracy scores over a state-of-the-art text super-resolution model TBSRN on the real-world low-resolution dataset TextZoom while having a smaller theoretical model size due to the usage of quantization techniques. In addition, we show how different training strategies influence the performance of the resulting model.
@inproceedings{hildebrandt2022optical, abstract = {Recognizing disturbed text in real-life images is a difficult problem, as information that is missing due to low resolution or out-of-focus text has to be recreated. Combining text super-resolution and optical character recognition deep learning models can be a valuable tool to enlarge and enhance text images for better readability, as well as recognize text automatically afterwards. We achieve improved peak signal-to-noise ratio and text recognition accuracy scores over a state-of-the-art text super-resolution model TBSRN on the real-world low-resolution dataset TextZoom while having a smaller theoretical model size due to the usage of quantization techniques. In addition, we show how different training strategies influence the performance of the resulting model.}, author = {Hildebrandt, Philipp and Schulze, Maximilian and Cohen, Sarel and Doskoč, Vanja and Saabni, Raid and Friedrich, Tobias}, booktitle = {Symposium on Document Engineering (DocEng)}, keywords = {sarelcohen vanjadoskoc philipphildebrandt maximilianschulze tobiasfriedrich doceng raidsaabni year2022}, pages = {1-4}, title = {Optical Character Recognition Guided Image Super Resolution}, year = 2022 }

Führlich, Pascal; Cseh, Ágnes; Lenzner, Pascal Improving Ranking Quality and Fairness in Swiss-System Chess TournamentsACM Conference on Economics and Computation (EC) 2022: 1101–1102
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
The International Chess Federation (FIDE) imposes a voluminous and complex set of player pairing criteria in Swiss-system chess tournaments and endorses computer programs that are able to calculate the prescribed pairings. The purpose of these formalities is to ensure that players are paired fairly during the tournament and that the final ranking corresponds to the players' true strength order. We contest the official FIDE player pairing routine by presenting alternative pairing rules. These can be enforced by computing maximum weight matchings in a carefully designed graph. We demonstrate by extensive experiments that a tournament format using our mechanism (1) yields fairer pairings in the rounds of the tournament and (2) produces a final ranking that reflects the players' true strengths better than the state-of-the-art FIDE pairing system.
@inproceedings{fuhrlich2022improving, abstract = {The International Chess Federation (FIDE) imposes a voluminous and complex set of player pairing criteria in Swiss-system chess tournaments and endorses computer programs that are able to calculate the prescribed pairings. The purpose of these formalities is to ensure that players are paired fairly during the tournament and that the final ranking corresponds to the players' true strength order. We contest the official FIDE player pairing routine by presenting alternative pairing rules. These can be enforced by computing maximum weight matchings in a carefully designed graph. We demonstrate by extensive experiments that a tournament format using our mechanism (1) yields fairer pairings in the rounds of the tournament and (2) produces a final ranking that reflects the players' true strengths better than the state-of-the-art FIDE pairing system.}, author = {Führlich, Pascal and Cseh, Ágnes and Lenzner, Pascal}, booktitle = {ACM Conference on Economics and Computation (EC)}, keywords = {agnescseh year2022 ec pascallenzner}, pages = {1101 &ndash; 1102}, publisher = {ACM}, title = {Improving Ranking Quality and Fairness in Swiss-System Chess Tournaments}, year = 2022 }

Bläsius, Thomas; Fischbeck, Philipp On the External Validity of Average-Case Analyses of Graph AlgorithmsEuropean Symposium on Algorithms (ESA) 2022: 21:1–21:14
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
The number one criticism of average-case analysis is that we do not actually know the probability distribution of real-world inputs. Thus, analyzing an algorithm on some random model has no implications for practical performance. At its core, this criticism doubts the existence of external validity, i.e., it assumes that algorithmic behavior on the somewhat simple and clean models does not translate beyond the models to practical performance real-world input. With this paper, we provide a first step towards studying the question of external validity systematically. To this end, we evaluate the performance of six graph algorithms on a collection of 2751 sparse real-world networks depending on two properties; the heterogeneity (variance in the degree distribution) and locality (tendency of edges to connect vertices that are already close). We compare this with the performance on generated networks with varying locality and heterogeneity. We find that the performance in the idealized setting of network models translates surprisingly well to real-world networks. Moreover, heterogeneity and locality appear to be the core properties impacting the performance of many graph algorithms.
@inproceedings{blasius2022external, abstract = {The number one criticism of average-case analysis is that we do not actually know the probability distribution of real-world inputs. Thus, analyzing an algorithm on some random model has no implications for practical performance. At its core, this criticism doubts the existence of external validity, i.e., it assumes that algorithmic behavior on the somewhat simple and clean models does not translate beyond the models to practical performance real-world input. With this paper, we provide a first step towards studying the question of external validity systematically. To this end, we evaluate the performance of six graph algorithms on a collection of 2751 sparse real-world networks depending on two properties; the heterogeneity (variance in the degree distribution) and locality (tendency of edges to connect vertices that are already close). We compare this with the performance on generated networks with varying locality and heterogeneity. We find that the performance in the idealized setting of network models translates surprisingly well to real-world networks. Moreover, heterogeneity and locality appear to be the core properties impacting the performance of many graph algorithms.}, author = {Bläsius, Thomas and Fischbeck, Philipp}, booktitle = {European Symposium on Algorithms (ESA)}, keywords = {philippfischbeck esa thomasblaesius year2022}, pages = {21:1&ndash;21:14}, title = {On the External Validity of Average-Case Analyses of Graph Algorithms}, year = 2022 }

Kumar, Nikhil An Approximate Generalization of the Okamura-Seymour TheoremSymposium on Foundations of Computer Science (FOCS) 2022
[ Abstract ] [ BibTeX ] [ Download ]
 
We consider the problem of multicommodity flows in planar graphs. Okamura and Seymour showed that if all the demands are incident on one face, then the cut-condition is sufficient for routing demands. We consider the following generalization of this setting and prove an approximate max flow-min cut theorem: for every demand edge, there exists a face containing both its end points. We show that the cut-condition is sufficient for routing \(\Omega(1)\)-fraction of all the demands. To prove this, we give a \(L_1\)-embedding of the planar metric which approximately preserves distance between all pair of points on the same face.
@inproceedings{kumar2022approximate, abstract = {We consider the problem of multicommodity flows in planar graphs. Okamura and Seymour showed that if all the demands are incident on one face, then the cut-condition is sufficient for routing demands. We consider the following generalization of this setting and prove an approximate max flow-min cut theorem: for every demand edge, there exists a face containing both its end points. We show that the cut-condition is sufficient for routing \(\Omega(1)\)-fraction of all the demands. To prove this, we give a \(L_1\)-embedding of the planar metric which approximately preserves distance between all pair of points on the same face.}, author = {Kumar, Nikhil}, booktitle = {Symposium on Foundations of Computer Science (FOCS)}, keywords = {sys:relevantfor:ae nikhilkumar focs year2022}, title = {An Approximate Generalization of the Okamura-Seymour Theorem}, year = 2022 }

Angrick, Sebastian; Bals, Ben; Hastrich, Niko; Kleissl, Maximilian; Schmidt, Jonas; Doskoč, Vanja; Katzmann, Maximilian; Molitor, Louise; Friedrich, Tobias Towards Explainable Real Estate Valuation via Evolutionary AlgorithmsGenetic and Evolutionary Computation Conference (GECCO) 2022: 1130–1138
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Human lives are increasingly influenced by algorithms, which therefore need to meet higher standards not only in accuracy but also with respect to explainability. This is especially true for high-stakes areas such as real estate valuation. Unfortunately, the methods applied there often exhibit a trade-off between accuracy and explainability. One explainable approach is case-based reasoning (CBR), whereeach decision is supported by specific previous cases. However, such methods can be wanting in accuracy. The unexplainable machine learning approaches are often observed to provide higher accuracy but are not scrutable in their decision-making. In this paper, we apply evolutionary algorithms (EAs) to CBR predictors in order to improve their performance. In particular, we deploy EAs to the similarity functions (used in CBR to find comparable cases), which are fitted to the data set at hand. As a consequence, we achieve higher accuracy than state-of-the-art deep neural networks (DNNs), while keeping interpretability and explainability. These results stem from our empirical evaluation on a large data set of real estate offers where we compare known similarity functions, their EA-improved counterparts, and DNNs. Surprisingly, DNNs are only on par with standard CBR techniques. However, using EA-learned similarity functions does yield an improved performance.
@inproceedings{angrick2022towards, abstract = {Human lives are increasingly influenced by algorithms, which therefore need to meet higher standards not only in accuracy but also with respect to explainability. This is especially true for high-stakes areas such as real estate valuation. Unfortunately, the methods applied there often exhibit a trade-off between accuracy and explainability. One explainable approach is case-based reasoning (CBR), whereeach decision is supported by specific previous cases. However, such methods can be wanting in accuracy. The unexplainable machine learning approaches are often observed to provide higher accuracy but are not scrutable in their decision-making. In this paper, we apply evolutionary algorithms (EAs) to CBR predictors in order to improve their performance. In particular, we deploy EAs to the similarity functions (used in CBR to find comparable cases), which are fitted to the data set at hand. As a consequence, we achieve higher accuracy than state-of-the-art deep neural networks (DNNs), while keeping interpretability and explainability. These results stem from our empirical evaluation on a large data set of real estate offers where we compare known similarity functions, their EA-improved counterparts, and DNNs. Surprisingly, DNNs are only on par with standard CBR techniques. However, using EA-learned similarity functions does yield an improved performance.}, author = {Angrick, Sebastian and Bals, Ben and Hastrich, Niko and Kleissl, Maximilian and Schmidt, Jonas and Doskoč, Vanja and Katzmann, Maximilian and Molitor, Louise and Friedrich, Tobias}, booktitle = {Genetic and Evolutionary Computation Conference (GECCO)}, keywords = {louisemolitor vanjadoskoc sebastianangrick benbals nikohastrich tobiasfriedrich gecco maximiliankleissl jonasschmidt maximiliankatzmann year2022}, pages = {1130&ndash;1138}, title = {Towards Explainable Real Estate Valuation via Evolutionary Algorithms}, year = 2022 }

Baguley, Samuel; Friedrich, Tobias; Timo, Kötzing; Li, Xiaoyue; Pappik, Marcus; Zeif, Ziena Analysis of a Gray-Box Operator for Vertex CoverGenetic and Evolutionary Computation Conference (GECCO) 2022: 1363–1371
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Combinatorial optimization problems are a prominent application area of evolutionary algorithms, where the (1+1) EA is one of the most investigated. We extend this algorithm by introducing some problem knowledge with a specialized mutation operator which works under the assumption that the number of 1s of a solution is critical, as frequently happens in combinatorial optimization. This slight modification increases the chance to correct wrongly placed bits while preserving the simplicity and problem independence of the (1+1) EA. As an application of our algorithm we examine the vertex cover problem on certain instances, where we show that it leads to asymptotically better runtimes and even finds with higher probability optimal solutions in comparison with the usual (1+1) EA. Precisely, we compare the performance of both algorithms on paths and on complete bipartite graphs of size \(n\). Regarding the path we prove that, for a particular initial configuration, the (1+1) EA takes in expectation \(\Theta(n^4)\) iterations while the modification reduces this to \(\Theta(n^3)\), and present experimental evidence that such a configuration is reached. Concerning the complete bipartite graph our modification finds the optimum in polynomial time with probability \(1-1/2^{\Omega(n^\xi)}\) for every positive constant \(\xi < 1\), which improves the known probability of \(1-1/\)poly\((n)\) for the (1+1) EA.
@inproceedings{baguley2022analysis, abstract = {Combinatorial optimization problems are a prominent application area of evolutionary algorithms, where the (1+1) EA is one of the most investigated. We extend this algorithm by introducing some problem knowledge with a specialized mutation operator which works under the assumption that the number of 1s of a solution is critical, as frequently happens in combinatorial optimization. This slight modification increases the chance to correct wrongly placed bits while preserving the simplicity and problem independence of the (1+1) EA. As an application of our algorithm we examine the vertex cover problem on certain instances, where we show that it leads to asymptotically better runtimes and even finds with higher probability optimal solutions in comparison with the usual (1+1) EA. Precisely, we compare the performance of both algorithms on paths and on complete bipartite graphs of size \(n\). Regarding the path we prove that, for a particular initial configuration, the (1+1) EA takes in expectation \(\Theta(n^4)\) iterations while the modification reduces this to \(\Theta(n^3)\), and present experimental evidence that such a configuration is reached. Concerning the complete bipartite graph our modification finds the optimum in polynomial time with probability \(1-1/2^{\Omega(n^\xi)}\) for every positive constant \(\xi < 1\), which improves the known probability of \(1-1/\)poly\((n)\) for the (1+1) EA.}, author = {Baguley, Samuel and Friedrich, Tobias and Timo, Kötzing and Li, Xiaoyue and Pappik, Marcus and Zeif, Ziena}, booktitle = {Genetic and Evolutionary Computation Conference (GECCO)}, keywords = {sys:relevantfor:ae zienazeif marcuspappik samuelbaguley xiaoyueli timokoetzing tobiasfriedrich gecco year2022}, pages = {1363&ndash;1371}, title = {Analysis of a Gray-Box Operator for Vertex Cover}, year = 2022 }

Friedrich, Tobias; Kötzing, Timo; Radhakrishnan, Aishwarya; Schiller, Leon; Schirneck, Martin; Tennigkeit, Georg; Wietheger, Simon Crossover for Cardinality Constrained OptimizationGenetic and Evolutionary Computation Conference (GECCO) 2022: 1399–1407
Best Paper Award (Theory Track)
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
In order to understand better how and why crossover can benefit optimization, we consider pseudo-Boolean functions with an upper bound \(B\) on the number of 1s allowed in the bit string (cardinality constraint). We consider the natural translation of the OneMax test function, a linear function where \(B\) bits have a weight of \(1+\varepsilon\) and the remaining bits have a weight of \(1\). The literature gives a bound of \(\Theta(n^2)\) for the (1+1) EA on this function. Part of the difficulty when optimizing this problem lies in having to improve individuals meeting the cardinality constraint by flipping both a 1 and a 0. The experimental literature proposes balanced operators, preserving the number of 1s, as a remedy. We show that a balanced mutation operator optimizes the problem in \(O(n \log n)\) if \(n-B = O(1)\). However, if \(n-B = \Theta(n)\), we show a bound of \(\Omega(n^2)\), just as classic bit flip mutation. Crossover and a simple island model gives \(O(n^2 / \log n)\) (uniform crossover) and \(O(n\sqrt{n})\) (3-ary majority vote crossover). For balanced uniform crossover with Hamming distance maximization for diversity we show a bound of \(O(n \log n)\). As an additional contribution we analyze and discuss different balanced crossover operators from the literature.
@inproceedings{friedrich2022crossover, abstract = {In order to understand better how and why crossover can benefit optimization, we consider pseudo-Boolean functions with an upper bound \(B\) on the number of 1s allowed in the bit string (cardinality constraint). We consider the natural translation of the OneMax test function, a linear function where \(B\) bits have a weight of \(1+\varepsilon\) and the remaining bits have a weight of \(1\). The literature gives a bound of \(\Theta(n^2)\) for the (1+1) EA on this function. Part of the difficulty when optimizing this problem lies in having to improve individuals meeting the cardinality constraint by flipping both a 1 and a 0. The experimental literature proposes balanced operators, preserving the number of 1s, as a remedy. We show that a balanced mutation operator optimizes the problem in \(O(n \log n)\) if \(n-B = O(1)\). However, if \(n-B = \Theta(n)\), we show a bound of \(\Omega(n^2)\), just as classic bit flip mutation. Crossover and a simple island model gives \(O(n^2 / \log n)\) (uniform crossover) and \(O(n\sqrt{n})\) (3-ary majority vote crossover). For balanced uniform crossover with Hamming distance maximization for diversity we show a bound of \(O(n \log n)\). As an additional contribution we analyze and discuss different balanced crossover operators from the literature.}, author = {Friedrich, Tobias and Kötzing, Timo and Radhakrishnan, Aishwarya and Schiller, Leon and Schirneck, Martin and Tennigkeit, Georg and Wietheger, Simon}, booktitle = {Genetic and Evolutionary Computation Conference (GECCO)}, keywords = {aishwaryaradhakrishnan timokoetzing simonwietheger tobiasfriedrich gecco leonschiller year2022 georgtennigkeit martinschirneck}, note = {Best Paper Award (Theory Track)}, pages = {1399&ndash;1407}, title = {Crossover for Cardinality Constrained Optimization}, year = 2022 }

Wood, Andrew; Hershcovitch, Moshik; Ennmouri, Ilias; Zong, Weiyu; Chennuri, Saurav; Cohen, Sarel; Sundararaman, Swaminathan; Waddington, Daniel; Chin, Peter Towards Fast Crash-Consistent Cluster CheckpointingHigh Performance Extreme Computing Conference (HPEC) 2022
[ Abstract ] [ BibTeX ] [ Download ]
 
Machine Learning models are expensive to train: they require expensive high-compute hardware and have long training times. Therefore, models are extra sensitive to program faults or unexpected system crashes, which can erase hours if not days worth of work. While there are plenty of strategies designed to mitigate the risk of unexpected system downtime, the most popular strategy in machine learning is called checkpointing: periodically saving the state of the model to persistent storage. Checkpointing is an effective strategy, however, it requires carefully balancing two operations: how often a checkpoint is made (the checkpointing schedule), and the cost of creating a checkpoint itself. In this paper, we leverage Python Memory Manager (PyMM), which provides Python support for Persistent Memory and emerging Persistent Memory technology (Optane DC) to accelerate the checkpointing operation while maintaining crash consistency. We first show that when checkpointing models, PyMM with persistent memory can save from minutes to days of checkpointing runtime. We then further optimize the checkpointing operation with PyMM and demonstrate our approach with the KMeans and Gaussian Mixture Model algorithms on two real-world datasets: MNIST and MusicNet. Through evaluation, we show that these two algorithms achieve a checkpointing speedup of a factor between 10 and 75x for KMeans and over 3x for GMM against the current state-of-the-art checkpointing approaches. We also verify that our solution recovers from crashes, while traditional approaches cannot.
@inproceedings{wood2022towards, abstract = {Machine Learning models are expensive to train: they require expensive high-compute hardware and have long training times. Therefore, models are extra sensitive to program faults or unexpected system crashes, which can erase hours if not days worth of work. While there are plenty of strategies designed to mitigate the risk of unexpected system downtime, the most popular strategy in machine learning is called checkpointing: periodically saving the state of the model to persistent storage. Checkpointing is an effective strategy, however, it requires carefully balancing two operations: how often a checkpoint is made (the checkpointing schedule), and the cost of creating a checkpoint itself. In this paper, we leverage Python Memory Manager (PyMM), which provides Python support for Persistent Memory and emerging Persistent Memory technology (Optane DC) to accelerate the checkpointing operation while maintaining crash consistency. We first show that when checkpointing models, PyMM with persistent memory can save from minutes to days of checkpointing runtime. We then further optimize the checkpointing operation with PyMM and demonstrate our approach with the KMeans and Gaussian Mixture Model algorithms on two real-world datasets: MNIST and MusicNet. Through evaluation, we show that these two algorithms achieve a checkpointing speedup of a factor between 10 and 75x for KMeans and over 3x for GMM against the current state-of-the-art checkpointing approaches. We also verify that our solution recovers from crashes, while traditional approaches cannot.}, author = {Wood, Andrew and Hershcovitch, Moshik and Ennmouri, Ilias and Zong, Weiyu and Chennuri, Saurav and Cohen, Sarel and Sundararaman, Swaminathan and Waddington, Daniel and Chin, Peter}, booktitle = {High Performance Extreme Computing Conference (HPEC)}, keywords = {sarelcohen hpec year2022}, title = {Towards Fast Crash-Consistent Cluster Checkpointing}, year = 2022 }

Friedrich, Tobias; Gawendowicz, Hans; Lenzner, Pascal; Melnichenko, Anna Social Distancing Network CreationInternational Colloquium on Automata, Languages and Programming (ICALP) 2022: 62:1–62:21
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
During a pandemic people have to find a trade-off between meeting others and staying safely at home. While meeting others is pleasant, it also increases the risk of infection. We consider this dilemma by introducing a game-theoretic network creation model in which selfish agents can form bilateral connections. They benefit from network neighbors, but at the same time, they want to maximize their distance to all other agents. This models the inherent conflict that social distancing rules impose on the behavior of selfish agents in a social network. Besides addressing this familiar issue, our model can be seen as the inverse to the well-studied Network Creation Game by Fabrikant et al.~[PODC 2003] where agents aim at being as central as possible in the created network. Thus, our work is in-line with studies that compare minimization problems with their maximization versions. We look at two variants of network creation governed by social distancing. In the first variant, there are no restrictions on the connections being formed. We characterize optimal and equilibrium networks, and we derive asymptotically tight bounds on the Price of Anarchy and Price of Stability. The second variant is the model's generalization that allows restrictions on the connections that can be formed. As our main result, we prove that Swap-Maximal Routing-Cost Spanning Trees, an efficiently computable weaker variant of Maximum Routing-Cost Spanning Trees, actually resemble equilibria for a significant range of the parameter space. Moreover, we give almost tight bounds on the Price of Anarchy and Price of Stability. These results imply that, compared the well-studied inverse models, under social distancing the agents' selfish behavior has a significantly stronger impact on the quality of the equilibria, i.e., allowing socially much worse stable states.
@inproceedings{friedrich2022social, abstract = {During a pandemic people have to find a trade-off between meeting others and staying safely at home. While meeting others is pleasant, it also increases the risk of infection. We consider this dilemma by introducing a game-theoretic network creation model in which selfish agents can form bilateral connections. They benefit from network neighbors, but at the same time, they want to maximize their distance to all other agents. This models the inherent conflict that social distancing rules impose on the behavior of selfish agents in a social network. Besides addressing this familiar issue, our model can be seen as the inverse to the well-studied Network Creation Game by Fabrikant et al.&nbsp;[PODC 2003] where agents aim at being as central as possible in the created network. Thus, our work is in-line with studies that compare minimization problems with their maximization versions. We look at two variants of network creation governed by social distancing. In the first variant, there are no restrictions on the connections being formed. We characterize optimal and equilibrium networks, and we derive asymptotically tight bounds on the Price of Anarchy and Price of Stability. The second variant is the model's generalization that allows restrictions on the connections that can be formed. As our main result, we prove that Swap-Maximal Routing-Cost Spanning Trees, an efficiently computable weaker variant of Maximum Routing-Cost Spanning Trees, actually resemble equilibria for a significant range of the parameter space. Moreover, we give almost tight bounds on the Price of Anarchy and Price of Stability. These results imply that, compared the well-studied inverse models, under social distancing the agents' selfish behavior has a significantly stronger impact on the quality of the equilibria, i.e., allowing socially much worse stable states.}, author = {Friedrich, Tobias and Gawendowicz, Hans and Lenzner, Pascal and Melnichenko, Anna}, booktitle = {International Colloquium on Automata, Languages and Programming (ICALP)}, keywords = {hansgawendowicz tobiasfriedrich icalp annamelnichenko year2022 pascallenzner}, pages = {62:1&ndash;62:21}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum f{{ü}}r Informatik}, title = {Social Distancing Network Creation}, volume = {LIPIcs:229}, year = 2022 }

Bilò, Davide; Choudhary, Keerti; Cohen, Sarel; Friedrich, Tobias; Schirneck, Martin Deterministic Sensitivity Oracles for Diameter, Eccentricities and All Pairs DistancesInternational Colloquium on Automata, Languages and Programming (ICALP) 2022: 68:1–68:19
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
We construct data structures for extremal and pairwise distances in directed graphs in the presence of transient edge failures. Henzinger et al. (ITCS 2017) initiated the study of fault-tolerant (sensitivity) oracles for the diameter and vertex eccentricities. We extend this with a special focus on space efficiency. We present several new data structures, among them the first fault-tolerant eccentricity oracle for dual failures in subcubic space. We further prove lower bounds that show limits to approximation vs. space and diameter vs. space trade-offs for fault-tolerant oracles. They highlight key differences between data structures for undirected and directed graphs. Initially, our oracles are randomized leaning on a sampling technique frequently used in sensitivity analysis. Building on the work of Alon, Chechik, and Cohen (ICALP 2019) as well as Karthik and Parter (SODA 2021), we develop a hierarchical framework to derandomize fault-tolerant data structures. We first apply it to our own diameter/eccentricity oracles and then show its usefulness by derandomizing algorithms from the literature: the distance sensitivity oracle of Ren (JCSS 2022) and the Single-Source Replacement Path algorithm of Chechik and Magen (ICALP 2020).
@inproceedings{bilo2022deterministic, abstract = {We construct data structures for extremal and pairwise distances in directed graphs in the presence of transient edge failures. Henzinger et al. (ITCS 2017) initiated the study of fault-tolerant (sensitivity) oracles for the diameter and vertex eccentricities. We extend this with a special focus on space efficiency. We present several new data structures, among them the first fault-tolerant eccentricity oracle for dual failures in subcubic space. We further prove lower bounds that show limits to approximation vs. space and diameter vs. space trade-offs for fault-tolerant oracles. They highlight key differences between data structures for undirected and directed graphs. Initially, our oracles are randomized leaning on a sampling technique frequently used in sensitivity analysis. Building on the work of Alon, Chechik, and Cohen (ICALP 2019) as well as Karthik and Parter (SODA 2021), we develop a hierarchical framework to derandomize fault-tolerant data structures. We first apply it to our own diameter/eccentricity oracles and then show its usefulness by derandomizing algorithms from the literature: the distance sensitivity oracle of Ren (JCSS 2022) and the Single-Source Replacement Path algorithm of Chechik and Magen (ICALP 2020).}, author = {Bilò, Davide and Choudhary, Keerti and Cohen, Sarel and Friedrich, Tobias and Schirneck, Martin}, booktitle = {International Colloquium on Automata, Languages and Programming (ICALP)}, keywords = {sarelcohen davidebilo tobiasfriedrich icalp keertichoudhary year2022 martinschirneck}, pages = {68:1-68:19}, title = {Deterministic Sensitivity Oracles for Diameter, Eccentricities and All Pairs Distances}, year = 2022 }

Böther, Maximilian; Kißig, Otto; Taraz, Martin; Cohen, Sarel; Seidel, Karen; Friedrich, Tobias What’s Wrong with Deep Learning in Tree Search for Combinatorial OptimizationInternational Conference on Learning Representations (ICLR) 2022
[ Abstract ] [ BibTeX ] [ URL ] [ Download ]
 
Combinatorial optimization lies at the core of many real-world problems. Especially since the rise of graph neural networks (GNNs), the deep learning community has been developing solvers that derive solutions to NP-hard problems by learning the problem-specific solution structure. However, reproducing the results of these publications proves to be difficult. We make three contributions. First, we present an open-source benchmark suite for the NP-hard Maximum Independent Set problem, in both its weighted and unweighted variants. The suite offers a unified interface to various state-of-the-art traditional and machine learning-based solvers. Second, using our benchmark suite, we conduct an in-depth analysis of the popular guided tree search algorithm by Li et al. [NeurIPS 2018], testing various configurations on small and large synthetic and real-world graphs. By re-implementing their algorithm with a focus on code quality and extensibility, we show that the graph convolution network used in the tree search does not learn a meaningful representation of the solution structure, and can in fact be replaced by random values. Instead, the tree search relies on algorithmic techniques like graph kernelization to find good solutions. Thus, the results from the original publication are not reproducible. Third, we extend the analysis to compare the tree search implementations to other solvers, showing that the classical algorithmic solvers often are faster, while providing solutions of similar quality. Additionally, we analyze a recent solver based on reinforcement learning and observe that for this solver, the GNN is responsible for the competitive solution quality.
@inproceedings{bother2022whats, abstract = {Combinatorial optimization lies at the core of many real-world problems. Especially since the rise of graph neural networks (GNNs), the deep learning community has been developing solvers that derive solutions to NP-hard problems by learning the problem-specific solution structure. However, reproducing the results of these publications proves to be difficult. We make three contributions. First, we present an open-source benchmark suite for the NP-hard Maximum Independent Set problem, in both its weighted and unweighted variants. The suite offers a unified interface to various state-of-the-art traditional and machine learning-based solvers. Second, using our benchmark suite, we conduct an in-depth analysis of the popular guided tree search algorithm by Li et al. [NeurIPS 2018], testing various configurations on small and large synthetic and real-world graphs. By re-implementing their algorithm with a focus on code quality and extensibility, we show that the graph convolution network used in the tree search does not learn a meaningful representation of the solution structure, and can in fact be replaced by random values. Instead, the tree search relies on algorithmic techniques like graph kernelization to find good solutions. Thus, the results from the original publication are not reproducible. Third, we extend the analysis to compare the tree search implementations to other solvers, showing that the classical algorithmic solvers often are faster, while providing solutions of similar quality. Additionally, we analyze a recent solver based on reinforcement learning and observe that for this solver, the GNN is responsible for the competitive solution quality.}, author = {Böther, Maximilian and Kißig, Otto and Taraz, Martin and Cohen, Sarel and Seidel, Karen and Friedrich, Tobias}, booktitle = {International Conference on Learning Representations (ICLR)}, keywords = {maximilianboether sarelcohen ottokissig tobiasfriedrich martintaraz year2022 iclr karenseidel}, title = {What’s Wrong with Deep Learning in Tree Search for Combinatorial Optimization}, year = 2022 }

Bilò, Davide; Bilò, Vittorio; Lenzner, Pascal; Molitor, Louise Tolerance is Necessary for Stability: Single-Peaked Swap Schelling GamesInternational Joint Conference on Artificial Intelligence (IJCAI) 2022: 81–87
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Residential segregation in metropolitan areas is a phenomenon that can be observed all over the world. Recently, this was investigated via game-theoretic models. There, selfish agents of two types are equipped with a monotone utility function that ensures higher utility if an agent has more same-type neighbors. The agents strategically choose their location on a given graph that serves as residential area to maximize their utility. However, sociological polls suggest that real-world agents are actually favoring mixed-type neighborhoods, and hence should be modeled via non-monotone utility functions. To address this, we study Swap Schelling Games with single-peaked utility functions. Our main finding is that tolerance, i.e., agents favoring fifty-fifty neighborhoods or being in the minority, is necessary for equilibrium existence on almost regular or bipartite graphs. Regarding the quality of equilibria, we derive (almost) tight bounds on the Price of Anarchy and the Price of Stability. In particular, we show that the latter is constant on bipartite and almost regular graphs.
@inproceedings{bilo2022tolerance, abstract = {Residential segregation in metropolitan areas is a phenomenon that can be observed all over the world. Recently, this was investigated via game-theoretic models. There, selfish agents of two types are equipped with a monotone utility function that ensures higher utility if an agent has more same-type neighbors. The agents strategically choose their location on a given graph that serves as residential area to maximize their utility. However, sociological polls suggest that real-world agents are actually favoring mixed-type neighborhoods, and hence should be modeled via non-monotone utility functions. To address this, we study Swap Schelling Games with single-peaked utility functions. Our main finding is that tolerance, i.e., agents favoring fifty-fifty neighborhoods or being in the minority, is necessary for equilibrium existence on almost regular or bipartite graphs. Regarding the quality of equilibria, we derive (almost) tight bounds on the Price of Anarchy and the Price of Stability. In particular, we show that the latter is constant on bipartite and almost regular graphs.}, author = {Bilò, Davide and Bilò, Vittorio and Lenzner, Pascal and Molitor, Louise}, booktitle = {International Joint Conference on Artificial Intelligence (IJCAI)}, keywords = {ijcai louisemolitor year2022 pascallenzner}, pages = {81&ndash;87}, publisher = {ijcai.org}, title = {Tolerance is Necessary for Stability: Single-Peaked Swap Schelling Games}, year = 2022 }

Bullinger, Martin; Lenzner, Pascal; Melnichenko, Anna Network Creation with Homophilic AgentsInternational Joint Conference on Artificial Intelligence (IJCAI) 2022: 151–157
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Network Creation Games are an important framework for understanding the formation of real-world networks such as social networks. These games usually assume a set of indistinguishable agents strategically buying edges at a uniform price leading to a network among them. However, in real life, agents are heterogeneous and their relationships often display a bias towards similar agents, say of the same ethnic group. This homophilic behavior on the agent level can then lead to the emergent global phenomenon of social segregation. We initiate the study of Network Creation Games with multiple types of homophilic agents and non-uniform edge cost. Specifically, we introduce and compare two models, focusing on the perception of same-type and different-type neighboring agents, respectively. Despite their different initial conditions, both our theoretical and experimental analysis show that the resulting equilibrium networks are almost identical in the two models, indicating a robust structure of social networks under homophily. Moreover, we investigate the segregation strength of the formed networks and thereby offer new insights on understanding segregation.
@inproceedings{bullinger2022network, abstract = {Network Creation Games are an important framework for understanding the formation of real-world networks such as social networks. These games usually assume a set of indistinguishable agents strategically buying edges at a uniform price leading to a network among them. However, in real life, agents are heterogeneous and their relationships often display a bias towards similar agents, say of the same ethnic group. This homophilic behavior on the agent level can then lead to the emergent global phenomenon of social segregation. We initiate the study of Network Creation Games with multiple types of homophilic agents and non-uniform edge cost. Specifically, we introduce and compare two models, focusing on the perception of same-type and different-type neighboring agents, respectively. Despite their different initial conditions, both our theoretical and experimental analysis show that the resulting equilibrium networks are almost identical in the two models, indicating a robust structure of social networks under homophily. Moreover, we investigate the segregation strength of the formed networks and thereby offer new insights on understanding segregation.}, author = {Bullinger, Martin and Lenzner, Pascal and Melnichenko, Anna}, booktitle = {International Joint Conference on Artificial Intelligence (IJCAI)}, keywords = {ijcai annamelnichenko year2022 pascallenzner}, pages = {151&ndash;157}, publisher = {ijcai.org}, title = {Network Creation with Homophilic Agents}, year = 2022 }

Bilò, Davide; Casel, Katrin; Choudhary, Keerti; Cohen, Sarel; Friedrich, Tobias; Lagodzinski, J.A. Gregor; Schirneck, Martin; Wietheger, Simon Fixed-Parameter Sensitivity OraclesInnovations in Theoretical Computer Science (ITCS) 2022: 23:1–23:18
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
We combine ideas from distance sensitivity oracles (DSOs) and fixed-parameter tractability (FPT) to design sensitivity oracles for FPT graph problems. An oracle with sensitivity \(f\) for an FPT problem \(\Pi\) on a graph \(G\) with parameter \(k\) preprocesses \(G\) in time \(O(g(f,k) poly(n))\). When queried with a set \(F\) of at most \(f\) edges of \(G\), the oracle reports the answer to the \(\Pi\)-with the same parameter \(k\)-on the graph \(G-F\), i.e., \(G\) deprived of \(F\). The oracle should answer queries in a time that is significantly faster than merely running the best-known FPT algorithm on \(G-F\) from scratch. We design sensitivity oracles for the \(k\)-Path and the \(k\)-Vertex Cover problem. Our first oracle for \(k\)-Path has size \(O(k^{f+1})\) size and query time \(O(f \min\{f, log (f) + k\})\). We use a technique inspired by the work of Weimann and Yuster [FOCS 2010, TALG 2013] on distance sensitivity problems to reduce the space to \(O\big(\big(\frac{f+k}{f}\big)^f \big(\frac{f+k}{k}\big)^k fk \cdot \log n\big)\) at the expense of increasing the query time to \(O\big(\big(\frac{f+k}{f}\big)^f \big(\frac{f+k}{k}\big)^k f \min\{f,k\} \cdot \log n \big)\). Both oracles can be modified to handle vertex-failures, but we need to replace \(k\) with \(2k\) in all the claimed bounds. Regarding \(k\)-Vertex Cover, we design three oracles offering different trade-offs between the size and the query time. The first oracle takes \(O(3^{f+k})\) space and has \(O(2^f)\) query time, the second one has a size of \(O(2^{f+k^2+k})\) and a query time of \(O(f{+}k^2)\); finally, the third one takes \(O(fk+k^2)\) space and can be queried in time \(O(1.2738^k + fk^2)\). All our oracles are computable in time (at most) proportional to their size and the time needed to detect a \(k\)-path or \(k\)-vertex cover, respectively. We also provide an interesting connection between \(k\)-Vertex Cover and the fault-tolerant shortest path problem, by giving a DSO of size \(O(poly(f,k) \cdot n)\) with query time in \(O(poly(f,k))\), where \(k\) is the size of a vertex cover. Following our line of research connecting fault-tolerant FPT and shortest paths problems, we introduce parameterization to the computation of distance preservers. Given a graph with a fixed source \(s\) and parameters \(f\),\(k\), we study the problem of constructing polynomial-sized oracles that reports efficiently, for any target vertex \(v\) and set \(F\) of at most \(f\) edge failures, whether the distance from \(s\) to \(v\) increases at most by an additive term of \(k\) in \(G-F\). The oracle size is \(O(2^k k^2 \cdot n)\), while the time needed to answer a query is \(O(2^k f^\omega k^\omega)\), where \(\omega<2.373\) is the matrix multiplication exponent. The second problem we study is about the construction of bounded-stretch fault-tolerant preservers. We construct a subgraph with \(O(2^{fk+f+k k \cdot n)\) edges that preserves those \(s\)-\(v\)-distances that do not increase by more than \(k\) upon failure of \(F\). This improves significantly over the \( \tilde{O} (f n^{2-\frac{1}{2^f}}) \) bound in the unparameterized case by Bodwin et al. [ICALP 2017].
@inproceedings{bilo2022fixedparameter, abstract = {We combine ideas from distance sensitivity oracles (DSOs) and fixed-parameter tractability (FPT) to design sensitivity oracles for FPT graph problems. An oracle with sensitivity \(f\) for an FPT problem \(\Pi\) on a graph \(G\) with parameter \(k\) preprocesses \(G\) in time \(O(g(f,k) poly(n))\). When queried with a set \(F\) of at most \(f\) edges of \(G\), the oracle reports the answer to the \(\Pi\)-with the same parameter \(k\)-on the graph \(G-F\), i.e., \(G\) deprived of \(F\). The oracle should answer queries in a time that is significantly faster than merely running the best-known FPT algorithm on \(G-F\) from scratch. We design sensitivity oracles for the \(k\)-Path and the \(k\)-Vertex Cover problem. Our first oracle for \(k\)-Path has size \(O(k^{f+1})\) size and query time \(O(f \min\{f, \log (f) + k\})\). We use a technique inspired by the work of Weimann and Yuster [FOCS 2010, TALG 2013] on distance sensitivity problems to reduce the space to \(O\big(\big(\frac{f+k}{f}\big)^f \big(\frac{f+k}{k}\big)^k fk \cdot \log n\big)\) at the expense of increasing the query time to \(O\big(\big(\frac{f+k}{f}\big)^f \big(\frac{f+k}{k}\big)^k f \min\{f,k\} \cdot \log n \big)\). Both oracles can be modified to handle vertex-failures, but we need to replace \(k\) with \(2k\) in all the claimed bounds. Regarding \(k\)-Vertex Cover, we design three oracles offering different trade-offs between the size and the query time. The first oracle takes \(O(3^{f+k})\) space and has \(O(2^f)\) query time, the second one has a size of \(O(2^{f+k^2+k})\) and a query time of \(O(f{+}k^2)\); finally, the third one takes \(O(fk+k^2)\) space and can be queried in time \(O(1.2738^k + fk^2)\). All our oracles are computable in time (at most) proportional to their size and the time needed to detect a \(k\)-path or \(k\)-vertex cover, respectively. We also provide an interesting connection between \(k\)-Vertex Cover and the fault-tolerant shortest path problem, by giving a DSO of size \(O(poly(f,k) \cdot n)\) with query time in \(O(poly(f,k))\), where \(k\) is the size of a vertex cover. Following our line of research connecting fault-tolerant FPT and shortest paths problems, we introduce parameterization to the computation of distance preservers. Given a graph with a fixed source \(s\) and parameters \(f\),\(k\), we study the problem of constructing polynomial-sized oracles that reports efficiently, for any target vertex \(v\) and set \(F\) of at most \(f\) edge failures, whether the distance from \(s\) to \(v\) increases at most by an additive term of \(k\) in \(G-F\). The oracle size is \(O(2^k k^2 \cdot n)\), while the time needed to answer a query is \(O(2^k f^\omega k^\omega)\), where \(\omega<2.373\) is the matrix multiplication exponent. The second problem we study is about the construction of bounded-stretch fault-tolerant preservers. We construct a subgraph with \(O(2^{fk+f+k} k \cdot n)\) edges that preserves those \(s\)-\(v\)-distances that do not increase by more than \(k\) upon failure of \(F\). This improves significantly over the \( \tilde{O} (f n^{2-\frac{1}{2^f}}) \) bound in the unparameterized case by Bodwin et al. [ICALP 2017].}, author = {Bilò, Davide and Casel, Katrin and Choudhary, Keerti and Cohen, Sarel and Friedrich, Tobias and Lagodzinski, J.A. Gregor and Schirneck, Martin and Wietheger, Simon}, booktitle = {Innovations in Theoretical Computer Science (ITCS)}, keywords = {sarelcohen gregorlagodzinski davidebilo katrincasel simonwietheger tobiasfriedrich itcs keertichoudhary year2022 martinschirneck}, pages = {23:1-23:18}, title = {Fixed-Parameter Sensitivity Oracles}, year = 2022 }

Friedrich, Tobias; Kötzing, Timo; Krejca, Martin S.; Rajabi, Amirhossein Escaping Local Optima With Local Search: A Theory-Driven DiscussionParallel Problem Solving from Nature (PPSN) 2022: 442–455
Best Paper Award and Best Poster Award
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Local search is the most basic strategy in optimization settings when no specific problem knowledge is employed. While this strategy finds good solutions for certain optimization problems, it generally suffers from getting stuck in local optima. This stagnation can be avoided if local search is modified. Depending on the optimization landscape, different modifications vary in their success. We discuss several features of optimization landscapes and give analyses as examples for how they affect the performance of modifications of local search. We consider modifying random local search by restarting it and by considering larger search radii. The landscape features we analyze include the number of local optima, the distance between different optima, as well as the local landscape around a local optimum. For each feature, we show which modifications of local search handle them well and which do not.
@inproceedings{friedrich2022escaping, abstract = {Local search is the most basic strategy in optimization settings when no specific problem knowledge is employed. While this strategy finds good solutions for certain optimization problems, it generally suffers from getting stuck in local optima. This stagnation can be avoided if local search is modified. Depending on the optimization landscape, different modifications vary in their success. We discuss several features of optimization landscapes and give analyses as examples for how they affect the performance of modifications of local search. We consider modifying random local search by restarting it and by considering larger search radii. The landscape features we analyze include the number of local optima, the distance between different optima, as well as the local landscape around a local optimum. For each feature, we show which modifications of local search handle them well and which do not.}, author = {Friedrich, Tobias and Kötzing, Timo and Krejca, Martin S. and Rajabi, Amirhossein}, booktitle = {Parallel Problem Solving from Nature (PPSN)}, keywords = {martinskrejca timokoetzing tobiasfriedrich amirhosseinrajabi year2022 ppsn}, note = {Best Paper Award and Best Poster Award}, pages = {442-455}, title = {Escaping Local Optima With Local Search: A Theory-Driven Discussion}, year = 2022 }

Friedrich, Tobias; Kötzing, Timo; Neumann, Frank; Radhakrishnan, Aishwarya Theoretical Study of Optimizing Rugge Landscapes with the cGAParallel Problem Solving From Nature (PPSN) 2022: 586–599
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Estimation of distribution algorithms (EDAs) provide a distribution-based approach for optimization which adapts its probability distribution during the run of the algorithm. We contribute to the theoretical understanding of EDAs and point out that their distribution approach makes them more suitable to deal with rugged fitness landscapes than classical local search algorithms. Concretely, we make the OneMax function rugged by adding noise to each fitness value. The cGA can nevertheless find solutions with \(n (1 - \epsilon )\) many 1s, even for high variance of noise. In contrast to this, RLS and the (1+1) EA, with high probability, only find solutions with \(n(1/2 + o(1)) \) many 1s, even for noise with small variance.
@inproceedings{friedrich2022theoretical, abstract = {Estimation of distribution algorithms (EDAs) provide a distribution-based approach for optimization which adapts its probability distribution during the run of the algorithm. We contribute to the theoretical understanding of EDAs and point out that their distribution approach makes them more suitable to deal with rugged fitness landscapes than classical local search algorithms. Concretely, we make the OneMax function rugged by adding noise to each fitness value. The cGA can nevertheless find solutions with \(n (1 - \epsilon )\) many 1s, even for high variance of noise. In contrast to this, RLS and the (1+1) EA, with high probability, only find solutions with \(n(1/2 + o(1)) \) many 1s, even for noise with small variance.}, author = {Friedrich, Tobias and Kötzing, Timo and Neumann, Frank and Radhakrishnan, Aishwarya}, booktitle = {Parallel Problem Solving From Nature (PPSN)}, keywords = {aishwaryaradhakrishnan timokoetzing tobiasfriedrich frankneumann year2022 ppsn}, pages = {586–599}, title = {Theoretical Study of Optimizing Rugge Landscapes with the cGA}, year = 2022 }

Bläsius, Thomas; Fischbeck, Philipp; Gottesbüren, Lars; Hamann, Michael; Heuer, Tobias; Spinner, Jonas; Weyand, Christopher; Wilhelm, Marcus A Branch-and-Bound Algorithm for Cluster EditingSymposium on Experimental Algorithms (SEA) 2022: 13:1–13:19
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The editing problem asks to transform a given graph into a disjoint union of cliques by inserting and deleting as few edges as possible. We describe and evaluate an exact branch-and-bound algorithm for cluster editing. For this, we introduce new reduction rules and adapt existing ones. Moreover, we generalize a known packing technique to obtain lower bounds and experimentally show that it contributes significantly to the performance of the solver. Our experiments further evaluate the effectiveness of the different reduction rules and examine the effects of structural properties of the input graph on solver performance. Our solver won the exact track of the 2021 PACE challenge.
@inproceedings{blasius2022branchandbound, abstract = {The editing problem asks to transform a given graph into a disjoint union of cliques by inserting and deleting as few edges as possible. We describe and evaluate an exact branch-and-bound algorithm for cluster editing. For this, we introduce new reduction rules and adapt existing ones. Moreover, we generalize a known packing technique to obtain lower bounds and experimentally show that it contributes significantly to the performance of the solver. Our experiments further evaluate the effectiveness of the different reduction rules and examine the effects of structural properties of the input graph on solver performance. Our solver won the exact track of the 2021 PACE challenge.}, author = {Bläsius, Thomas and Fischbeck, Philipp and Gottesbüren, Lars and Hamann, Michael and Heuer, Tobias and Spinner, Jonas and Weyand, Christopher and Wilhelm, Marcus}, booktitle = {Symposium on Experimental Algorithms (SEA)}, keywords = {philippfischbeck larsgottesbueren thomasblaesius michaelhamann tobiasheuer christopherweyand year2022 marcuswilhelm jonasspinner sea}, pages = {13:1&ndash;13:19}, title = {A Branch-and-Bound Algorithm for Cluster Editing}, year = 2022 }

Cohen, Sarel; Fischbeck, Philipp; Friedrich, Tobias; Krejca, Martin S.; Sauerwald, Thomas Accelerated Information Dissemination on Networks with Local and Global EdgesStructural Information and Communication Complexity (SIROCCO) 2022: 79–97
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Bootstrap percolation is a classical model for the spread of information in a network. In the round-based version, nodes of an undirected graph become active once at least \(r\) neighbors were active in the previous round. We propose the \emph{perturbed percolation process: a superposition of two percolation processes on the same node set. One process acts on a local graph with activation threshold~\(1\), the other acts on a global graph with threshold \(r\)~-- representing local and global edges, respectively. We consider grid-like local graphs and expanders as global graphs on~\(n\) nodes. For the extreme case \(r = 1\), all nodes are active after \(O(\log n)\) rounds, while the process spreads only polynomially fast for the other extreme case \(r \geq n\). For a range of suitable values of~\(r\), we prove that the process exhibits both phases of the above extremes: It starts with a polynomial growth and eventually transitions from at most \(cn\) to~\(n\) active nodes, for some constant \(c in (0, 1)\), in \(O(\log n)\) rounds. We observe this behavior also empirically, considering additional global-graph models.
@inproceedings{cohen2022accelerated, abstract = {Bootstrap percolation is a classical model for the spread of information in a network. In the round-based version, nodes of an undirected graph become active once at least \(r\) neighbors were active in the previous round. We propose the \emph{perturbed} percolation process: a superposition of two percolation processes on the same node set. One process acts on a local graph with activation threshold&nbsp;\(1\), the other acts on a global graph with threshold \(r\)&nbsp;&ndash; representing local and global edges, respectively. We consider grid-like local graphs and expanders as global graphs on&nbsp;\(n\) nodes. For the extreme case \(r = 1\), all nodes are active after \(O(\log n)\) rounds, while the process spreads only polynomially fast for the other extreme case \(r \geq n\). For a range of suitable values of&nbsp;\(r\), we prove that the process exhibits both phases of the above extremes: It starts with a polynomial growth and eventually transitions from at most \(cn\) to&nbsp;\(n\) active nodes, for some constant \(c \in (0, 1)\), in \(O(\log n)\) rounds. We observe this behavior also empirically, considering additional global-graph models.}, author = {Cohen, Sarel and Fischbeck, Philipp and Friedrich, Tobias and Krejca, Martin S. and Sauerwald, Thomas}, booktitle = {Structural Information and Communication Complexity (SIROCCO)}, keywords = {sarelcohen philippfischbeck martinskrejca sirocco tobiasfriedrich year2022 thomassauerwald}, pages = {79&ndash;97}, title = {Accelerated Information Dissemination on Networks with Local and Global Edges}, year = 2022 }

Fomin, Fedor V.; Golovach, Petr A.; Sagunov, Danil; Simonov, Kirill Algorithmic Extensions of Dirac’s TheoremSymposium on Discrete Algorithms (SODA) 2022: 406–416
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We introduce a general method for obtaining fixed-parameter algorithms for problems about finding paths in undirected graphs, where the length of the path could be unbounded in the parameter. The first application of our method is a randomized algorithm, that given a colored \(n\)-vertex undirected graph, vertices \(s\) and \(t\), and an integer \(k\), finds an \((s,t)\)-path containing at least \(k\) different colors in time \(2^k n^\mathcal{O(1)}\). This is the first FPT algorithm for this problem, and it generalizes the algorithm of Björklund, Husfeldt, and Taslaman [SODA 2012] on finding a path through \(k\) specified vertices. It also implies the first \(2^k n^\mathcal{O(1)}\) time algorithm for finding an \(s,t)\)-path of length at least \(k\). Our method yields FPT algorithms for even more general problems. For example, we consider the problem where the input consists of an \(n\)-vertex undirected graph \(G\), a matroid \(M\) whose elements correspond to the vertices of \(G\) and which is represented over a finite field of order \(q\), a positive integer weight function on the vertices of \(G\), two sets of vertices \(S,T subseteq V(G)\), and integers \(p,k,w\), and the task is to find \(p\) vertex-disjoint paths from \(S\) to \(T\) so that the union of the vertices of these paths contains an independent set of \(M\) of cardinality \(k\) and weight \(w\), while minimizing the sum of the lengths of the paths. We give a \(2^{p+\mathcal{O(k^2 log (q+k)) n^\mathcal{O(1) w\) time randomized algorithm for this problem.
@inproceedings{fomin2022algorithmic, abstract = {We introduce a general method for obtaining fixed-parameter algorithms for problems about finding paths in undirected graphs, where the length of the path could be unbounded in the parameter. The first application of our method is a randomized algorithm, that given a colored \(n\)-vertex undirected graph, vertices \(s\) and \(t\), and an integer \(k\), finds an \((s,t)\)-path containing at least \(k\) different colors in time \(2^k n^{\mathcal{O}(1)}\). This is the first FPT algorithm for this problem, and it generalizes the algorithm of Bj{ö}rklund, Husfeldt, and Taslaman [SODA 2012] on finding a path through \(k\) specified vertices. It also implies the first \(2^k n^{\mathcal{O}(1)}\) time algorithm for finding an \(s,t)\)-path of length at least \(k\). Our method yields FPT algorithms for even more general problems. For example, we consider the problem where the input consists of an \(n\)-vertex undirected graph \(G\), a matroid \(M\) whose elements correspond to the vertices of \(G\) and which is represented over a finite field of order \(q\), a positive integer weight function on the vertices of \(G\), two sets of vertices \(S,T \subseteq V(G)\), and integers \(p,k,w\), and the task is to find \(p\) vertex-disjoint paths from \(S\) to \(T\) so that the union of the vertices of these paths contains an independent set of \(M\) of cardinality \(k\) and weight \(w\), while minimizing the sum of the lengths of the paths. We give a \(2^{p+\mathcal{O}(k^2 \log (q+k))} n^{\mathcal{O}(1)} w\) time randomized algorithm for this problem.}, author = {Fomin, Fedor V. and Golovach, Petr A. and Sagunov, Danil and Simonov, Kirill}, booktitle = {Symposium on Discrete Algorithms (SODA)}, keywords = {sys:relevantfor:ae kirillsimonov soda year2022}, pages = {406-416}, title = {Algorithmic Extensions of Dirac's Theorem}, year = 2022 }

Bazgan, Cristina; Casel, Katrin; Cazals, Pierre Dense Graph Partitioning on sparse and dense graphs.Scandinavian Workshop Algorithm Theory (SWAT) 2022
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We consider the problem of partitioning a graph into a non-fixed number of non-overlapping subgraphs of maximum density. The density of a partition is the sum of the densities of the subgraphs, where the density of a subgraph is its average degree, that is, the ratio of its number of edges and its number of vertices. This problem, called Dense Graph Partition, is known to be NP-hard on general graphs and polynomial-time solvable on trees, and polynomial-time 2-approximable. In this paper we study the restriction of Dense Graph Partition to particular sparse and dense graph classes. In particular, we prove that it is NP-hard on dense bipartite graphs as well as on cubic graphs. On dense graphs on \(n\) vertices, it is polynomial-time solvable on graphs with minimum degree \(n-3\) and NP-hard on \((n-4)\)-regular graphs. We prove that it is polynomial-time 4/3-approximable on cubic graphs and admits an efficient polynomial-time approximation scheme on graphs of minimum degree \(n-t\) for any constant \(t\geq 4\).
@inproceedings{bazgan2022dense, abstract = {We consider the problem of partitioning a graph into a non-fixed number of non-overlapping subgraphs of maximum density. The density of a partition is the sum of the densities of the subgraphs, where the density of a subgraph is its average degree, that is, the ratio of its number of edges and its number of vertices. This problem, called Dense Graph Partition, is known to be NP-hard on general graphs and polynomial-time solvable on trees, and polynomial-time 2-approximable. In this paper we study the restriction of Dense Graph Partition to particular sparse and dense graph classes. In particular, we prove that it is NP-hard on dense bipartite graphs as well as on cubic graphs. On dense graphs on \(n\) vertices, it is polynomial-time solvable on graphs with minimum degree \(n-3\) and NP-hard on \((n-4)\)-regular graphs. We prove that it is polynomial-time 4/3-approximable on cubic graphs and admits an efficient polynomial-time approximation scheme on graphs of minimum degree \(n-t\) for any constant \(t\geq 4\).}, author = {Bazgan, Cristina and Casel, Katrin and Cazals, Pierre}, booktitle = {Scandinavian Workshop Algorithm Theory (SWAT)}, keywords = {swat katrincasel year2022}, title = {Dense Graph Partitioning on sparse and dense graphs.}, year = 2022 }

2021

Göbel, Andreas; Lagodzinski, J. A. Gregor; Seidel, Karen Counting Homomorphisms to Trees Modulo a PrimeACM Transactions on Computation Theory 2021
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Many important graph theoretic notions can be encoded as counting graph homomorphism problems, such as partition functions in statistical physics, in particular independent sets and colourings. In this article we study the complexity of~\($\#_p\textsc{HomsTo}H$\), the problem of counting graph homomorphisms from an input graph to a graph \($H$\) modulo a prime number~\($p$\). Dyer and Greenhill proved a dichotomy stating that the tractability of non-modular counting graph homomorphisms depends on the structure of the target graph. Many intractable cases in non-modular counting become tractable in modular counting due to the common phenomenon of cancellation. In subsequent studies on counting modulo~\($2$\), however, the influence of the structure of~\($H$\) on the tractability was shown to persist, which yields similar dichotomies. Our main result states that for every tree~\($H$\) and every prime~\($p$\) the problem \($\#_p\textsc{HomsTo}H$\) is either polynomial time computable or \($\#_p\mathsf{P}$\)-complete. This relates to the conjecture of Faben and Jerrum stating that this dichotomy holds for every graph \($H$\) when counting modulo~2. In contrast to previous results on modular counting, the tractable cases of \($\#_p\textsc{HomsTo}H$\) are essentially the same for all values of the modulo when \($H$\) is a tree. To prove this result, we study the structural properties of a homomorphism. As an important interim result, our study yields a dichotomy for the problem of counting weighted independent sets in a bipartite graph modulo some prime~\($p$\). These results are the first suggesting that such dichotomies hold not only for the one-bit functions of the modulo~2 case but also for the modular counting functions of all primes~\($p$\).
@article{gobel2021counting, abstract = {Many important graph theoretic notions can be encoded as counting graph homomorphism problems, such as partition functions in statistical physics, in particular independent sets and colourings. In this article we study the complexity of&nbsp;$\#_p\textsc{HomsTo}H$, the problem of counting graph homomorphisms from an input graph to a graph $H$ modulo a prime number&nbsp;$p$. Dyer and Greenhill proved a dichotomy stating that the tractability of non-modular counting graph homomorphisms depends on the structure of the target graph. Many intractable cases in non-modular counting become tractable in modular counting due to the common phenomenon of cancellation. In subsequent studies on counting modulo&nbsp;$2$, however, the influence of the structure of&nbsp;$H$ on the tractability was shown to persist, which yields similar dichotomies. Our main result states that for every tree&nbsp;$H$ and every prime&nbsp;$p$ the problem $\#_p\textsc{HomsTo}H$ is either polynomial time computable or $\#_p\mathsf{P}$-complete. This relates to the conjecture of Faben and Jerrum stating that this dichotomy holds for every graph $H$ when counting modulo&nbsp;2. In contrast to previous results on modular counting, the tractable cases of $\#_p\textsc{HomsTo}H$ are essentially the same for all values of the modulo when $H$ is a tree. To prove this result, we study the structural properties of a homomorphism. As an important interim result, our study yields a dichotomy for the problem of counting weighted independent sets in a bipartite graph modulo some prime&nbsp;$p$. These results are the first suggesting that such dichotomies hold not only for the one-bit functions of the modulo&nbsp;2 case but also for the modular counting functions of all primes&nbsp;$p$.}, author = {Göbel, Andreas and Lagodzinski, J. A. Gregor and Seidel, Karen}, editor = {O'Donnell, Ryan}, journal = {ACM Transactions on Computation Theory}, keywords = {gregorlagodzinski andreasgoebel toct year2021 karenseidel}, month = {sep}, number = 3, title = {Counting Homomorphisms to Trees Modulo a Prime}, volume = 13, year = 2021 }

Cseh, Ágnes; Juhos, Attila Pairwise Preferences in the Stable Marriage ProblemACM Transactions on Economics and Computation (TEAC) 2021: 1–28
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We study the classical, two-sided stable marriage problem under pairwise preferences. In the most general setting, agents are allowed to express their preferences as comparisons of any two of their edges and they also have the right to declare a draw or even withdraw from such a comparison. This freedom is then gradually restricted as we specify six stages of orderedness in the preferences, ending with the classical case of strictly ordered lists. We study all cases occurring when combining the three known notions of stability—weak, strong and super-stability—under the assumption that each side of the bipartite market obtains one of the six degrees of orderedness. By designing three polynomial algorithms and two NP-completeness proofs we determine the complexity of all cases not yet known, and thus give an exact boundary in terms of preference structure between tractable and intractable cases.
@article{cseh2021pairwise, abstract = {We study the classical, two-sided stable marriage problem under pairwise preferences. In the most general setting, agents are allowed to express their preferences as comparisons of any two of their edges and they also have the right to declare a draw or even withdraw from such a comparison. This freedom is then gradually restricted as we specify six stages of orderedness in the preferences, ending with the classical case of strictly ordered lists. We study all cases occurring when combining the three known notions of stability—weak, strong and super-stability—under the assumption that each side of the bipartite market obtains one of the six degrees of orderedness. By designing three polynomial algorithms and two NP-completeness proofs we determine the complexity of all cases not yet known, and thus give an exact boundary in terms of preference structure between tractable and intractable cases.}, author = {Cseh, Ágnes and Juhos, Attila}, journal = {ACM Transactions on Economics and Computation (TEAC)}, keywords = {sys:relevantfor:ae agnescseh}, number = 1, pages = {1&ndash;28}, publisher = {ACM New York, NY, USA}, title = {Pairwise Preferences in the Stable Marriage Problem}, volume = 9, year = 2021 }

Cseh, Ágnes; Kavitha, Telikepalli Popular matchings in complete graphsAlgorithmica 2021: 1–31
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Our input is a complete graph \(G = (V,E)\) on n vertices where each vertex has a strict ranking of all other vertices in \(G\). The goal is to construct a matching in \(G\) that is "globally stable" or popular. A matching \(M\) is popular if \(M\) does not lose a head-to-head election against any matching \(M'\): here each vertex casts a vote for the matching in \(\{M,M'\}\) where it gets a better assignment. Popular matchings need not exist in the given instance \(G\) and the popular matching problem is to decide whether one exists or not. The popular matching problem in \(G\) is easy to solve for odd \(n\). Surprisingly, the problem becomes NP-hard for even n, as we show here.
@article{cseh2021popular, abstract = {Our input is a complete graph \(G = (V,E)\) on n vertices where each vertex has a strict ranking of all other vertices in \(G\). The goal is to construct a matching in \(G\) that is "globally stable" or popular. A matching \(M\) is popular if \(M\) does not lose a head-to-head election against any matching \(M'\): here each vertex casts a vote for the matching in \(\{M,M'\}\) where it gets a better assignment. Popular matchings need not exist in the given instance \(G\) and the popular matching problem is to decide whether one exists or not. The popular matching problem in \(G\) is easy to solve for odd \(n\). Surprisingly, the problem becomes NP-hard for even n, as we show here.}, author = {Cseh, Ágnes and Kavitha, Telikepalli}, journal = {Algorithmica}, keywords = {sys:relevantfor:ae agnescseh}, pages = {1&ndash;31}, publisher = {Springer}, title = {Popular matchings in complete graphs}, year = 2021 }

Andersson, Tommy; Cseh, Ágnes; Ehlers, Lars; Erlanson, Albin Organizing time exchanges: Lessons from matching marketsAmerican Economic Journal: Microeconomics 2021: 338–73
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This paper considers time exchanges via a common platform (e.g. , markets for exchanging time units, positions at education institutions, and tuition waivers). There are several problems associated with such markets, e.g., imbalanced outcomes, coordination problems, and inefficiencies. We model time exchanges as matching markets and construct a non-manipulable mec hanism that selects an individually rational and balanced allocation that maximizes exchanges among the participating agents (and those allocations are efficient). This mechanism works on a preference domain whereby agents classify the goods provided by other participating agents as either unacceptable or acceptable, and for goods classified as acceptable, agents have specific upper quotas representing their maximum needs.
@article{andersson2021organizing, abstract = {This paper considers time exchanges via a common platform (e.g. , markets for exchanging time units, positions at education institutions, and tuition waivers). There are several problems associated with such markets, e.g., imbalanced outcomes, coordination problems, and inefficiencies. We model time exchanges as matching markets and construct a non-manipulable mec hanism that selects an individually rational and balanced allocation that maximizes exchanges among the participating agents (and those allocations are efficient). This mechanism works on a preference domain whereby agents classify the goods provided by other participating agents as either unacceptable or acceptable, and for goods classified as acceptable, agents have specific upper quotas representing their maximum needs.}, author = {Andersson, Tommy and Cseh, Ágnes and Ehlers, Lars and Erlanson, Albin}, journal = {American Economic Journal: Microeconomics}, keywords = {sys:relevantfor:ae agnescseh}, number = 1, pages = {338&ndash;73}, title = {Organizing time exchanges: Lessons from matching markets}, volume = 13, year = 2021 }

Haemers, Willem H; Parsaei Majd, Leila Spectral symmetry in conference matricesDesigns, Codes and Cryptography 2021: 1–8
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A conference matrix of order \(n\) is an \(n \times n\) matrix \(C\) with diagonal entries \(0\) and off-diagonal entries \(\pm 1\) satisfying \(CC^T = (n - 1) I \). If \(C\) is symmetric, then \(C\) has a symmetric spectrum \(\sum\) (that is, \( \sum = - \sum \) ) and eigenvalues \(\pm \sqrt{n-1}\). We show that many principal submatrices of \(C\) also have symmetric spectrum, which leads to examples of Seidel matrices of graphs (or, equivalently, adjacency matrices of complete signed graphs) with a symmetric spectrum. In addition, we show that some Seidel matrices with symmetric spectrum can be characterized by this construction.
@article{haemers2021spectral, abstract = {A conference matrix of order \(n\) is an \(n \times n\) matrix \(C\) with diagonal entries \(0\) and off-diagonal entries \(\pm 1\) satisfying \(CC^T = (n - 1) I \). If \(C\) is symmetric, then \(C\) has a symmetric spectrum \(\sum\) (that is, \( \sum = - \sum \) ) and eigenvalues \(\pm \sqrt{n-1}\). We show that many principal submatrices of \(C\) also have symmetric spectrum, which leads to examples of Seidel matrices of graphs (or, equivalently, adjacency matrices of complete signed graphs) with a symmetric spectrum. In addition, we show that some Seidel matrices with symmetric spectrum can be characterized by this construction.}, author = {Haemers, Willem H and Parsaei Majd, Leila}, journal = {Designs, Codes and Cryptography}, keywords = {leilaparsaeimajd sys:relevantfor:ae willemhhaemers year2021}, pages = {1&ndash;8}, title = {Spectral symmetry in conference matrices}, year = 2021 }

Michail, Othon; Skretas, George; Spirakis, Paul G. Distributed computation and reconfiguration in actively dynamic networksDistributed Computing 2021: 185–206
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@article{michail2022distributed, author = {Michail, Othon and Skretas, George and Spirakis, Paul G.}, journal = {Distributed Computing}, keywords = {sys:relevantfor:ae distributed dynamic reconfiguration georgeskretas}, month = {dec}, pages = {185-206}, title = {Distributed computation and reconfiguration in actively dynamic networks}, volume = 35, year = 2021 }

Casel, Katrin; Fernau, Henning; Khosravian Ghadikolaei, Mehdi; Monnot, Jérôme; Sikora, Florian On the Complexity of Solution Extension of Optimization ProblemsTheoretical Computer Science 2021
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
The question if a given partial solution to a problem can be extended reasonably occurs in many algorithmic approaches for optimization problems. For instance, when enumerating minimal vertex covers of a graph G=(V,E), one usually arrives at the problem to decide for a vertex set \(U \subseteq V\) (pre-solution), if there exists a minimal vertex cover S (i.e., a vertex cover \(S \subseteq V\) such that no proper subset of S is a vertex cover) with \(U \subseteq S\) (minimal extension of U). We propose a general, partial-order based formulation of such extension problems which allows to model parameterization and approximation aspects of extension, and also highlights relationships between extension tasks for different specific problems. As examples, we study a number of specific problems which can be expressed and related in this framework. In particular, we discuss extension variants of the problems dominating set and feedback vertex/edge set. All these problems are shown to be NP-complete even when restricted to bipartite graphs of bounded degree, with the exception of our extension version of feedback edge set on undirected graphs which is shown to be solvable in polynomial time. For the extension variants of dominating and feedback vertex set, we also show NP-completeness for the restriction to planar graphs of bounded degree. As non-graph problem, we also study an extension version of the bin packing problem. We further consider the parameterized complexity of all these extension variants, where the parameter is a measure of the pre-solution as defined by our framework.
@article{casel2021complexity, abstract = {The question if a given partial solution to a problem can be extended reasonably occurs in many algorithmic approaches for optimization problems. For instance, when enumerating minimal vertex covers of a graph G=(V,E), one usually arrives at the problem to decide for a vertex set \(U \subseteq V\) (pre-solution), if there exists a minimal vertex cover S (i.e., a vertex cover \(S \subseteq V\) such that no proper subset of S is a vertex cover) with \(U \subseteq S\) (minimal extension of U). We propose a general, partial-order based formulation of such extension problems which allows to model parameterization and approximation aspects of extension, and also highlights relationships between extension tasks for different specific problems. As examples, we study a number of specific problems which can be expressed and related in this framework. In particular, we discuss extension variants of the problems dominating set and feedback vertex/edge set. All these problems are shown to be NP-complete even when restricted to bipartite graphs of bounded degree, with the exception of our extension version of feedback edge set on undirected graphs which is shown to be solvable in polynomial time. For the extension variants of dominating and feedback vertex set, we also show NP-completeness for the restriction to planar graphs of bounded degree. As non-graph problem, we also study an extension version of the bin packing problem. We further consider the parameterized complexity of all these extension variants, where the parameter is a measure of the pre-solution as defined by our framework.}, author = {Casel, Katrin and Fernau, Henning and Khosravian Ghadikolaei, Mehdi and Monnot, Jérôme and Sikora, Florian}, journal = {Theoretical Computer Science}, keywords = {tcs katrincasel year2021}, title = {On the Complexity of Solution Extension of Optimization Problems}, year = 2021 }

Doerr, Benjamin; Krejca, Martin S. A Simplified Run Time Analysis of the Univariate Marginal Distribution Algorithm on LeadingOnesTheoretical Computer Science 2021: 121–128
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With elementary means, we prove in this note a stronger run time guarantee for the univariate marginal distribution algorithm (UMDA) optimizing the LeadingOnes benchmark function in the desirable regime with low genetic drift. If the population size \(\mu\) is at least \(128 n \ln(n)\) and the selection rate \(\mu/\lambda\) is at most some constant less than \(\frac{1}{4e \approx 0.092\), then the UMDA samples the optimum within \(O\big(n\frac{\lambda}{log (\lambda/\mu)}\big)\) fitness evaluations with high probability. This improves over the previous \(O(n \lambda \log\lambda)\) guarantee that was obtained by Dang and Lehre (2015) via the deep level-based population method. With similar arguments as in our upper-bound analysis, we also obtain the first lower bound for this problem. Under similar assumptions, we prove that a bound of \(\Omega\big(lambda \frac{n - \log(n\lambda)}log (\lambda / \mu)}\big)\) fitness evaluations holds with high probability.
@article{doerr2021simplified, abstract = {With elementary means, we prove in this note a stronger run time guarantee for the univariate marginal distribution algorithm (UMDA) optimizing the LeadingOnes benchmark function in the desirable regime with low genetic drift. If the population size \(\mu\) is at least \(128 n \ln(n)\) and the selection rate \(\mu/\lambda\) is at most some constant less than \(\frac{1}{4e} \approx 0.092\), then the UMDA samples the optimum within \(O\big(n\frac{\lambda}{\log (\lambda/\mu)}\big)\) fitness evaluations with high probability. This improves over the previous \(O(n \lambda \log\lambda)\) guarantee that was obtained by Dang and Lehre (2015) via the deep level-based population method. With similar arguments as in our upper-bound analysis, we also obtain the first lower bound for this problem. Under similar assumptions, we prove that a bound of \(\Omega\big(\lambda \frac{n - \log(n\lambda)}{\log (\lambda / \mu)}\big)\) fitness evaluations holds with high probability.}, author = {Doerr, Benjamin and Krejca, Martin S.}, journal = {Theoretical Computer Science}, keywords = {tcs martinskrejca benjamindoerr year2021}, pages = {121-128}, title = {A Simplified Run Time Analysis of the Univariate Marginal Distribution Algorithm on LeadingOnes}, volume = 851, year = 2021 }

Bläsius, Thomas; Fischbeck, Philipp; Friedrich, Tobias; Katzmann, Maximilian Solving Vertex Cover in Polynomial Time on Hyperbolic Random GraphsTheory of Computing Systems 2021
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
The computational complexity of the VertexCover problem has been studied extensively. Most notably, it is NP-complete to find an optimal solution and typically NP-hard to find an approximation with reasonable factors. In contrast, recent experiments suggest that on many real-world networks the run time to solve VertexCover is way smaller than even the best known FPT-approaches can explain. We link these observations to two properties that are observed in many real-world networks, namely a heterogeneous degree distribution and high clustering. To formalize these properties and explain the observed behavior, we analyze how a branch-and-reduce algorithm performs on hyperbolic random graphs, which have become increasingly popular for modeling real-world networks. In fact, we are able to show that the VertexCover problem on hyperbolic random graphs can be solved in polynomial time, with high probability. The proof relies on interesting structural properties of hyperbolic random graphs. Since these predictions of the model are interesting in their own right, we conducted experiments on real-world networks showing that these properties are also observed in practice.
@article{bffk-svcpthrg-2021, abstract = {The computational complexity of the VertexCover problem has been studied extensively. Most notably, it is NP-complete to find an optimal solution and typically NP-hard to find an approximation with reasonable factors. In contrast, recent experiments suggest that on many real-world networks the run time to solve VertexCover is way smaller than even the best known FPT-approaches can explain. We link these observations to two properties that are observed in many real-world networks, namely a heterogeneous degree distribution and high clustering. To formalize these properties and explain the observed behavior, we analyze how a branch-and-reduce algorithm performs on hyperbolic random graphs, which have become increasingly popular for modeling real-world networks. In fact, we are able to show that the VertexCover problem on hyperbolic random graphs can be solved in polynomial time, with high probability. The proof relies on interesting structural properties of hyperbolic random graphs. Since these predictions of the model are interesting in their own right, we conducted experiments on real-world networks showing that these properties are also observed in practice.}, author = {Bläsius, Thomas and Fischbeck, Philipp and Friedrich, Tobias and Katzmann, Maximilian}, journal = {Theory of Computing Systems}, keywords = {philippfischbeck thomasblaesius tobiasfriedrich maximiliankatzmann tocs year2021}, title = {Solving Vertex Cover in Polynomial Time on Hyperbolic Random Graphs}, year = 2021 }

Casel, Katrin; Fernau, Henning; Gaspers, Serge; Gras, Benjamin; Schmid, Markus L. On the Complexity of the Smallest Grammar Problem over Fixed AlphabetsTheory of Computing Systems 2021: 344–409
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In the smallest grammar problem, we are given a word \(w\)and we want to compute a preferably small context-free grammar \(G\) for the singleton language \(\{w\}\) (where the size of a grammar is the sum of the sizes of its rules, and the size of a rule is measured by the length of its right side). It is known that, for unbounded alphabets, the decision variant of this problem is \(\mathsf{NP}\)-hard and the optimisation variant does not allow a polynomial-time approximation scheme, unless \(\mathsf{P}\) = \(\mathsf{NP}\). We settle the long-standing open problem whether these hardness results also hold for the more realistic case of a constant-size alphabet. More precisely, it is shown that the smallest grammar problem remains \(\mathsf{NP}\)-complete (and its optimisation version is \(\mathsf{APX}\)-hard), even if the alphabet is fixed and has size of at least 17. The corresponding reduction is robust in the sense that it also works for an alternative size-measure of grammars that is commonly used in the literature (i.e., a size measure also taking the number of rules into account), and it also allows to conclude that even computing the number of rules required by a smallest grammar is a hard problem. On the other hand, if the number of nonterminals (or, equivalently, the number of rules) is bounded by a constant, then the smallest grammar problem can be solved in polynomial time, which is shown by encoding it as a problem on graphs with interval structure. However, treating the number of rules as a parameter (in terms of parameterised complexity) yields \(\mathsf{W}\)[1]-hardness. Furthermore, we present an \(O(3^{|w|})\) exact exponential-time algorithm, based on dynamic programming. These three main questions are also investigated for 1-level grammars, i.e., grammars for which only the start rule contains nonterminals on the right side; thus, investigating the impact of the ``hierarchical depth'' of grammars on the complexity of the smallest grammar problem. In this regard, we obtain for 1-level grammars similar, but slightly stronger results.
@article{casel2020article, abstract = {In the smallest grammar problem, we are given a word \(w\)and we want to compute a preferably small context-free grammar \(G\) for the singleton language \(\{w\}\) (where the size of a grammar is the sum of the sizes of its rules, and the size of a rule is measured by the length of its right side). It is known that, for unbounded alphabets, the decision variant of this problem is \(\mathsf{NP}\)-hard and the optimisation variant does not allow a polynomial-time approximation scheme, unless \(\mathsf{P}\) = \(\mathsf{NP}\). We settle the long-standing open problem whether these hardness results also hold for the more realistic case of a constant-size alphabet. More precisely, it is shown that the smallest grammar problem remains \(\mathsf{NP}\)-complete (and its optimisation version is \(\mathsf{APX}\)-hard), even if the alphabet is fixed and has size of at least 17. The corresponding reduction is robust in the sense that it also works for an alternative size-measure of grammars that is commonly used in the literature (i.e., a size measure also taking the number of rules into account), and it also allows to conclude that even computing the number of rules required by a smallest grammar is a hard problem. On the other hand, if the number of nonterminals (or, equivalently, the number of rules) is bounded by a constant, then the smallest grammar problem can be solved in polynomial time, which is shown by encoding it as a problem on graphs with interval structure. However, treating the number of rules as a parameter (in terms of parameterised complexity) yields \(\mathsf{W}\)[1]-hardness. Furthermore, we present an \(O(3^{|w|})\) exact exponential-time algorithm, based on dynamic programming. These three main questions are also investigated for 1-level grammars, i.e., grammars for which only the start rule contains nonterminals on the right side; thus, investigating the impact of the ``hierarchical depth'' of grammars on the complexity of the smallest grammar problem. In this regard, we obtain for 1-level grammars similar, but slightly stronger results.}, author = {Casel, Katrin and Fernau, Henning and Gaspers, Serge and Gras, Benjamin and Schmid, Markus L.}, editor = {Springer}, journal = {Theory of Computing Systems}, keywords = {markuslschmid katrincasel benjamingras sergegaspers tocs henningfernau year2020}, number = 2, pages = {344–409}, title = {On the Complexity of the Smallest Grammar Problem over Fixed Alphabets}, volume = 65, year = 2021 }

Neubert, Stefan Grundkurs Theoretische Informatik Rheinwerk Computing 2021
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@book{neubert2021grundkurs, author = {Neubert, Stefan}, keywords = {stefanneubert year2021}, publisher = {Rheinwerk Computing}, title = {Grundkurs Theoretische Informatik}, year = 2021 }

Boockmeyer, Arne; Fischbeck, Philipp; Neubert, Stefan Fit fürs Studium - Informatik Rheinwerk Computing 2021
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@book{boockmeyer2021studium, author = {Boockmeyer, Arne and Fischbeck, Philipp and Neubert, Stefan}, edition = {Second}, keywords = {philippfischbeck arneboockmeyer stefanneubert year2021}, publisher = {Rheinwerk Computing}, title = {Fit fürs Studium - Informatik}, year = 2021 }

Aziz, Haris; Cseh, Agnes; Dickerson, John; McElfresh, Duncan Optimal Kidney Exchange with ImmunosuppressantsConference on Artificial Intelligence (AAAI) 2021: 21–29
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Algorithms for exchange of kidneys is one of the key successful applications in market design, artificial intelligence, and operations research. Potent immunosuppressant drugs suppress the body's ability to reject a transplanted organ up to the point that a transplant across blood- or tissue-type incompatibility becomes possible. In contrast to the standard kidney exchange problem, we consider a setting that also involves the decision about which recipients receive from the limited supply of immunosuppressants that make them compatible with originally incompatible kidneys. We firstly present a general computational framework to model this problem. Our main contribution is a range of efficient algorithms that provide flexibility in terms of meeting meaningful objectives. Motivated by the current reality of kidney exchanges using sophisticated mathematical-programming-based clearing algorithms, we then present a general but scalable approach to optimal clearing with immunosuppression; we validate our approach on realistic data from a large fielded exchange.
@inproceedings{haris2021optimal, abstract = {Algorithms for exchange of kidneys is one of the key successful applications in market design, artificial intelligence, and operations research. Potent immunosuppressant drugs suppress the body's ability to reject a transplanted organ up to the point that a transplant across blood- or tissue-type incompatibility becomes possible. In contrast to the standard kidney exchange problem, we consider a setting that also involves the decision about which recipients receive from the limited supply of immunosuppressants that make them compatible with originally incompatible kidneys. We firstly present a general computational framework to model this problem. Our main contribution is a range of efficient algorithms that provide flexibility in terms of meeting meaningful objectives. Motivated by the current reality of kidney exchanges using sophisticated mathematical-programming-based clearing algorithms, we then present a general but scalable approach to optimal clearing with immunosuppression; we validate our approach on realistic data from a large fielded exchange.}, author = {Aziz, Haris and Cseh, Agnes and Dickerson, John and McElfresh, Duncan}, booktitle = {Conference on Artificial Intelligence (AAAI)}, keywords = {johndickerson harisaziz agnescseh aaai duncanmcelfresh year2021}, pages = {21-29}, title = {Optimal Kidney Exchange with Immunosuppressants}, year = 2021 }

Bilò, Davide; Friedrich, Tobias; Lenzner, Pascal; Lowski, Stefanie; Melnichenko, Anna Selfish Creation of Social NetworksConference on Artificial Intelligence (AAAI) 2021: 5185–5193
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Understanding real-world networks has been a core research endeavor throughout the last two decades. Network Creation Games are a promising approach for this from a game-theoretic perspective. In these games, selfish agents corresponding to nodes in a network strategically decide which links to form to optimize their centrality. Many versions have been introduced and analyzed, but none of them fits to modeling the evolution of social networks. In real-world social networks, connections are often established by recommendations from common acquaintances or by a chain of such recommendations. Thus establishing and maintaining a contact with a friend of a friend is easier than connecting to complete strangers. This explains the high clustering, i.e., the abundance of triangles, in real-world social networks. We propose and analyze a network creation model inspired by real-world social networks. Edges are formed in our model via bilateral consent of both endpoints and the cost for establishing and maintaining an edge is proportional to the distance of the endpoints before establishing the connection. We provide results for generic cost functions, which essentially only must be convex functions in the distance of the endpoints without the respective edge. For this broad class of cost functions, we provide many structural properties of equilibrium networks and prove (almost) tight bounds on the diameter, the Price of Anarchy and the Price of Stability. Moreover, as a proof-of-concept we show via experiments that the created equilibrium networks of our model indeed closely mimics real-world social networks. We observe degree distributions that seem to follow a power-law, high clustering, and low diameters. This can be seen as a promising first step towards game-theoretic network creation models that predict networks featuring all core real-world properties.
@inproceedings{bilo2021selfish, abstract = {Understanding real-world networks has been a core research endeavor throughout the last two decades. Network Creation Games are a promising approach for this from a game-theoretic perspective. In these games, selfish agents corresponding to nodes in a network strategically decide which links to form to optimize their centrality. Many versions have been introduced and analyzed, but none of them fits to modeling the evolution of social networks. In real-world social networks, connections are often established by recommendations from common acquaintances or by a chain of such recommendations. Thus establishing and maintaining a contact with a friend of a friend is easier than connecting to complete strangers. This explains the high clustering, i.e., the abundance of triangles, in real-world social networks. We propose and analyze a network creation model inspired by real-world social networks. Edges are formed in our model via bilateral consent of both endpoints and the cost for establishing and maintaining an edge is proportional to the distance of the endpoints before establishing the connection. We provide results for generic cost functions, which essentially only must be convex functions in the distance of the endpoints without the respective edge. For this broad class of cost functions, we provide many structural properties of equilibrium networks and prove (almost) tight bounds on the diameter, the Price of Anarchy and the Price of Stability. Moreover, as a proof-of-concept we show via experiments that the created equilibrium networks of our model indeed closely mimics real-world social networks. We observe degree distributions that seem to follow a power-law, high clustering, and low diameters. This can be seen as a promising first step towards game-theoretic network creation models that predict networks featuring all core real-world properties.}, author = {Bilò, Davide and Friedrich, Tobias and Lenzner, Pascal and Lowski, Stefanie and Melnichenko, Anna}, booktitle = {Conference on Artificial Intelligence (AAAI)}, keywords = {davidebilo stefanielowski tobiasfriedrich aaai annamelnichenko pascallenzner year2021}, pages = {5185-5193}, title = {Selfish Creation of Social Networks}, year = 2021 }

Aziz, Haris; Chan, Hau; Cseh, Ágnes; Li, Bo; Ramezani, Fahimeh; Wang, Chenhao Multi-Robot Task Allocation—Complexity and ApproximationAutonomous Agents and Multiagent Systems (AAMAS) 2021: 133–141
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Multi-robot task allocation is one of the most fundamental classes of problems in robotics and is crucial for various real-world robotic applications such as search, rescue and area exploration. We consider the Single-Task robots and Multi-Robot tasks Instantaneous Assignment (ST-MR-IA) setting where each task requires at least a certain number of robots and each robot can work on at most one task and incurs an operational cost for each task. Our aim is to consider a natural computational problem of allocating robots to complete the maximum number of tasks subject to budget constraints. We consider budget constraints of three different kinds: (1) total budget, (2) task budget, and (3) robot budget. We provide a detailed complexity analysis including results on approximations as well as polynomial-time algorithms for the general setting and important restricted settings.
@inproceedings{aziz2021multirobot, abstract = {Multi-robot task allocation is one of the most fundamental classes of problems in robotics and is crucial for various real-world robotic applications such as search, rescue and area exploration. We consider the Single-Task robots and Multi-Robot tasks Instantaneous Assignment (ST-MR-IA) setting where each task requires at least a certain number of robots and each robot can work on at most one task and incurs an operational cost for each task. Our aim is to consider a natural computational problem of allocating robots to complete the maximum number of tasks subject to budget constraints. We consider budget constraints of three different kinds: (1) total budget, (2) task budget, and (3) robot budget. We provide a detailed complexity analysis including results on approximations as well as polynomial-time algorithms for the general setting and important restricted settings.}, author = {Aziz, Haris and Chan, Hau and Cseh, Ágnes and Li, Bo and Ramezani, Fahimeh and Wang, Chenhao}, booktitle = {Autonomous Agents and Multiagent Systems (AAMAS)}, keywords = {chenhaowang hauchan fahimehramezani boli harisaziz agnescseh aamas year2021}, pages = {133-141}, title = {Multi-Robot Task Allocation—Complexity and Approximation}, year = 2021 }

Kraiczy, Sonja; Cseh, Ágnes; Manlove, David On Weakly and Strongly Popular RankingsAutonomous Agents and Multiagent Systems (AAMAS) 2021: 1563–1565
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Van Zuylen et al. introduced the notion of a popular ranking in a voting context, where each voter submits a strictly-ordered list of all candidates. A popular ranking pi of the candidates is at least as good as any other ranking sigma in the following sense: if we compare pi to sigma, at least half of all voters will always weakly prefer pi. Whether a voter prefers one ranking to another is calculated based on the Kendall distance. A more traditional definition of popularity---as applied to popular matchings, a well-established topic in computational social choice---is stricter, because it requires at least half of the voters who are not indifferent between pi and sigma to prefer pi. In this paper, we derive structural and algorithmic results in both settings, also improving upon the results by van Zylen et al. We also point out connections to the famous open problem of finding a Kemeny consensus with 3 voters.
@inproceedings{kraiczy2021weakly, abstract = {Van Zuylen et al. introduced the notion of a popular ranking in a voting context, where each voter submits a strictly-ordered list of all candidates. A popular ranking pi of the candidates is at least as good as any other ranking sigma in the following sense: if we compare pi to sigma, at least half of all voters will always weakly prefer pi. Whether a voter prefers one ranking to another is calculated based on the Kendall distance. A more traditional definition of popularity&mdash;as applied to popular matchings, a well-established topic in computational social choice&mdash;is stricter, because it requires at least half of the voters who are not indifferent between pi and sigma to prefer pi. In this paper, we derive structural and algorithmic results in both settings, also improving upon the results by van Zylen et al. We also point out connections to the famous open problem of finding a Kemeny consensus with 3 voters.}, author = {Kraiczy, Sonja and Cseh, Ágnes and Manlove, David}, booktitle = {Autonomous Agents and Multiagent Systems (AAMAS)}, keywords = {davidfmanlove sonjakraiczy agnescseh aamas year2021}, pages = {1563-1565}, title = {On Weakly and Strongly Popular Rankings}, year = 2021 }

Cooley, Madison; Greene, Casey; Issac, Davis; Pividori, Milton; Sullivan, Blair Parameterized Algorithms for Identifying Gene Co-Expression Modules via Weighted Clique DecompositionApplied and Computational Discrete Algorithms (ACDA) 2021: 111–122
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
We present a new combinatorial model for identifying regulatory modules in gene co-expression data using a decomposition into weighted cliques. To capture complex interaction effects, we generalize the previously-studied weighted edge clique partition problem. As a first step, we restrict ourselves to the noise-free setting, and show that the problem is fixed parameter tractable when parameterized by the number of modules (cliques). We present two new algorithms for finding these decompositions, using linear programming and integer partitioning to determine the clique weights. Further, we implement these algorithms in Python and test them on a biologically-inspired synthetic corpus generated using real-world data from transcription factors and a latent variable analysis of co-expression in varying cell types.
@inproceedings{cooley2021parameterized, abstract = {We present a new combinatorial model for identifying regulatory modules in gene co-expression data using a decomposition into weighted cliques. To capture complex interaction effects, we generalize the previously-studied weighted edge clique partition problem. As a first step, we restrict ourselves to the noise-free setting, and show that the problem is fixed parameter tractable when parameterized by the number of modules (cliques). We present two new algorithms for finding these decompositions, using linear programming and integer partitioning to determine the clique weights. Further, we implement these algorithms in Python and test them on a biologically-inspired synthetic corpus generated using real-world data from transcription factors and a latent variable analysis of co-expression in varying cell types.}, author = {Cooley, Madison and Greene, Casey and Issac, Davis and Pividori, Milton and Sullivan, Blair}, booktitle = {Applied and Computational Discrete Algorithms (ACDA)}, keywords = {sys:relevantfor:ae blairsullivan acda miltonpividori davisissac madisoncooley year2021 caseygreene}, pages = {111-122}, title = {Parameterized Algorithms for Identifying Gene Co-Expression Modules via Weighted Clique Decomposition}, year = 2021 }

Quinzan, Francesco; Doskoč, Vanja; Göbel, Andreas; Friedrich, Tobias Adaptive Sampling for Fast Constrained Maximization of Submodular FunctionsArtificial Intelligence and Statistics (AISTATS) 2021: 964–972
[ Abstract ] [ BibTeX ] [ URL ] [ Download ]
 
Several large-scale machine learning tasks, such as data summarization, can be approached by maximizing functions that satisfy submodularity. These optimization problems often involve complex side constraints, imposed by the underlying application. In this paper, we develop an algorithm with poly-logarithmic adaptivity for non-monotone submodular maximization under general side constraints. The adaptive complexity of a problem is the minimal number of sequential rounds required to achieve the objective. Our algorithm is suitable to maximize a non-monotone submodular function under a \(p\)-system side constraint, and it achieves a \((p + O({\sqrt{p}}))\)-approximation for this problem, after only poly-logarithmic adaptive rounds and polynomial queries to the valuation oracle function. Furthermore, our algorithm achieves a \(p + O(1))\)-approximation when the given side constraint is a \(p\)-extendible system. This algorithm yields an exponential speed-up, with respect to the adaptivity, over any other known constant-factor approximation algorithm for this problem. It also competes with previous known results in terms of the query complexity. We perform various experiments on various real-world applications. We find that, in comparison with commonly used heuristics, our algorithm performs better on these instances.
@inproceedings{doskoc2021adaptive, abstract = {Several large-scale machine learning tasks, such as data summarization, can be approached by maximizing functions that satisfy submodularity. These optimization problems often involve complex side constraints, imposed by the underlying application. In this paper, we develop an algorithm with poly-logarithmic adaptivity for non-monotone submodular maximization under general side constraints. The adaptive complexity of a problem is the minimal number of sequential rounds required to achieve the objective. Our algorithm is suitable to maximize a non-monotone submodular function under a \(p\)-system side constraint, and it achieves a \((p + O({\sqrt{p}}))\)-approximation for this problem, after only poly-logarithmic adaptive rounds and polynomial queries to the valuation oracle function. Furthermore, our algorithm achieves a \(p + O(1))\)-approximation when the given side constraint is a \(p\)-extendible system. This algorithm yields an exponential speed-up, with respect to the adaptivity, over any other known constant-factor approximation algorithm for this problem. It also competes with previous known results in terms of the query complexity. We perform various experiments on various real-world applications. We find that, in comparison with commonly used heuristics, our algorithm performs better on these instances.}, author = {Quinzan, Francesco and Doskoč, Vanja and Göbel, Andreas and Friedrich, Tobias}, booktitle = {Artificial Intelligence and Statistics (AISTATS)}, keywords = {aistats vanjadoskoc andreasgoebel francescoquinzan tobiasfriedrich year2021}, pages = {964-972}, title = {Adaptive Sampling for Fast Constrained Maximization of Submodular Functions}, year = 2021 }

Borndörfer, Ralf; Casel, Katrin; Issac, Davis; Niklanovits, Aikaterini; Schwartz, Stephan; Zeif, Ziena Connected k-Partition of k-Connected Graphs and c-Claw-Free GraphsApproximation Algorithms for Combinatorial Optimization Problems (APPROX) 2021: 27:1–27:14
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
A connected partition is a partition of the vertices of a graph into sets that induce connected subgraphs. Such partitions naturally occur in many application areas such as road networks, and image processing. In these settings, it is often desirable to partition into a fixed number of parts of roughly of the same size or weight. The resulting computational problem is called Balanced Connected Partition (BCP). The two classical objectives for BCP are to maximize the weight of the smallest, or minimize the weight of the largest component. We study BCP on \(c\)-claw-free graphs, the class of graphs that do not have \(K_{1,c}\) as an induced subgraph, and present efficient \((c-1)\)-approximation algorithms for both objectives. In particular, for \(3\)-claw-free graphs, also simply known as claw-free graphs, we obtain a \(2\)-approximation. Due to the claw-freeness of line graphs, this also implies a \(2\)-approximation for the edge-partition version of BCP in general graphs. A harder connected partition problem arises from demanding a connected partition into k parts that have (possibly) heterogeneous target weights \(w_1, \dots, w_k\). In the 1970s Győri and Lovász showed that if \(G\) is \(k\)-connected and the target weights sum to the total size of \(G\), such a partition exists. However, to this day no polynomial algorithm to compute such partitions exists for \(k > 4\). Towards finding such a partition \(T_1, \dots, T_k\) in \(k\)-connected graphs for general \(k\), we show how to efficiently compute connected partitions that at least approximately meet the target weights, subject to the mild assumption that each \(w_i\) is greater than the weight of the heaviest vertex. In particular, we give a \(3\)-approximation for both the lower and the upper bounded version i.e. we guarantee that each \(T_i\) has weight at least \(\frac{w_i}{3}\) or that each \(T_i\) has weight most \(3 w_i\), respectively. Also, we present a both-side bounded version that produces a connected partition where each \(T_i\) has size at least \(\frac{w_i}{3}\) and at most \(\max(\{r, 3\}) w_i \), where \(r \geq 1\) is the ratio between the largest and smallest value in \(w_1, \dots, w_k\). In particular for the balanced version, i.e. \(w_1 = w_2 =, \dots , = w k\), this gives a partition with \(\frac{w_i3 leq w(T_i) \leq 3 w_i\).
@inproceedings{borndorfer2021connected, abstract = {A connected partition is a partition of the vertices of a graph into sets that induce connected subgraphs. Such partitions naturally occur in many application areas such as road networks, and image processing. In these settings, it is often desirable to partition into a fixed number of parts of roughly of the same size or weight. The resulting computational problem is called Balanced Connected Partition (BCP). The two classical objectives for BCP are to maximize the weight of the smallest, or minimize the weight of the largest component. We study BCP on \(c\)-claw-free graphs, the class of graphs that do not have \(K_{1,c}\) as an induced subgraph, and present efficient \((c-1)\)-approximation algorithms for both objectives. In particular, for \(3\)-claw-free graphs, also simply known as claw-free graphs, we obtain a \(2\)-approximation. Due to the claw-freeness of line graphs, this also implies a \(2\)-approximation for the edge-partition version of BCP in general graphs. A harder connected partition problem arises from demanding a connected partition into k parts that have (possibly) heterogeneous target weights \(w_1, \dots, w_k\). In the 1970s Győri and Lovász showed that if \(G\) is \(k\)-connected and the target weights sum to the total size of \(G\), such a partition exists. However, to this day no polynomial algorithm to compute such partitions exists for \(k > 4\). Towards finding such a partition \(T_1, \dots, T_k\) in \(k\)-connected graphs for general \(k\), we show how to efficiently compute connected partitions that at least approximately meet the target weights, subject to the mild assumption that each \(w_i\) is greater than the weight of the heaviest vertex. In particular, we give a \(3\)-approximation for both the lower and the upper bounded version i.e. we guarantee that each \(T_i\) has weight at least \(\frac{w_i}{3}\) or that each \(T_i\) has weight most \(3 w_i\), respectively. Also, we present a both-side bounded version that produces a connected partition where each \(T_i\) has size at least \(\frac{w_i}{3}\) and at most \(\max(\{r, 3\}) w_i \), where \(r \geq 1\) is the ratio between the largest and smallest value in \(w_1, \dots, w_k\). In particular for the balanced version, i.e. \(w_1 = w_2 =, \dots , = w k\), this gives a partition with \(\frac{w_i}{3} \leq w(T_i) \leq 3 w_i\).}, author = {Borndörfer, Ralf and Casel, Katrin and Issac, Davis and Niklanovits, Aikaterini and Schwartz, Stephan and Zeif, Ziena}, booktitle = {Approximation Algorithms for Combinatorial Optimization Problems (APPROX)}, keywords = {sys:relevantfor:ae zienazeif katrincasel davisissac aikaterininiklanovits approx year2021 ralfborndörfer stephanschwartz}, pages = {27:1-27:14}, title = {Connected k-Partition of k-Connected Graphs and c-Claw-Free Graphs}, year = 2021 }

Berger, Julian; Böther, Maximilian; Doskoč, Vanja; Gadea Harder, Jonathan; Klodt, Nicolas; Kötzing, Timo; Lötzsch, Winfried; Peters, Jannik; Schiller, Leon; Seifert, Lars; Wells, Armin; Wietheger, Simon Learning Languages with Decidable HypothesesComputability in Europe (CiE) 2021: 25–37
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
In \emph{language learning in the limit, the most common type of hypothesis is to give an enumerator for a language, a \(W\)-index. These hypotheses have the drawback that even the membership problem is undecidable. In this paper, we use a different system which allows for naming arbitrary decidable languages, namely \emph{programs for characteristic functions (called \(C\)-indices). These indices have the drawback that it is now not decidable whether a given hypothesis is even a legal \(C\)-index. In this first analysis of learning with \(C\)-indices, we give a structured account of the learning power of various restrictions employing \(C\)-indices, also when compared with \(W\)-indices. We establish a hierarchy of learning power depending on whether \(C\)-indices are required (a) on all outputs; (b) only on outputs relevant for the class to be learned or (c) only in the limit as final, correct hypotheses. We analyze all these questions also in relation to the mode of data presentation. Finally, we also ask about the relation of semantic versus syntactic convergence and derive the map of pairwise relations for these two kinds of convergence coupled with various forms of data presentation.
@inproceedings{berger2021learning, abstract = {In \emph{language learning in the limit}, the most common type of hypothesis is to give an enumerator for a language, a \(W\)-index. These hypotheses have the drawback that even the membership problem is undecidable. In this paper, we use a different system which allows for naming arbitrary decidable languages, namely \emph{programs for characteristic functions} (called \(C\)-indices). These indices have the drawback that it is now not decidable whether a given hypothesis is even a legal \(C\)-index. In this first analysis of learning with \(C\)-indices, we give a structured account of the learning power of various restrictions employing \(C\)-indices, also when compared with \(W\)-indices. We establish a hierarchy of learning power depending on whether \(C\)-indices are required (a) on all outputs; (b) only on outputs relevant for the class to be learned or (c) only in the limit as final, correct hypotheses. We analyze all these questions also in relation to the mode of data presentation. Finally, we also ask about the relation of semantic versus syntactic convergence and derive the map of pairwise relations for these two kinds of convergence coupled with various forms of data presentation.}, author = {Berger, Julian and Böther, Maximilian and Doskoč, Vanja and Gadea Harder, Jonathan and Klodt, Nicolas and Kötzing, Timo and Lötzsch, Winfried and Peters, Jannik and Schiller, Leon and Seifert, Lars and Wells, Armin and Wietheger, Simon}, booktitle = {Computability in Europe (CiE)}, keywords = {maximilianboether nicolasklodt vanjadoskoc simonwietheger larsseifert arminwells timokoetzing jannikpeters julianberger leonschiller winfriedloetzsch year2021 cie jonathangadeaharder}, pages = {25-37}, title = {Learning Languages with Decidable Hypotheses}, year = 2021 }

Doskoč, Vanja; Kötzing, Timo Mapping Monotonic Restrictions in Inductive InferenceComputability in Europe (CiE) 2021: 146–157
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In \emph{inductive inference we investigate computable devices (learners) learning formal languages. In this work, we focus on \emph{monotonic learners which, despite their natural motivation, exhibit peculiar behaviour. A recent study analysed the learning capabilities of \emph{strongly monotone learners in various settings. The therein unveiled differences between \emph{explanatory (syntactically converging) and \emph{behaviourally correct (semantically converging) such learners motivate our studies of \emph{monotone learners in the same settings. While the structure of the pairwise relations for monotone explanatory learning is similar to the strongly monotone case (and for similar reasons), for behaviourally correct learning a very different picture emerges. In the latter setup, we provide a \emph{self-learning class of languages showing that monotone learners, as opposed to their strongly monotone counterpart, do heavily rely on the order in which the information is given, an unusual result for behaviourally correct learners.
@inproceedings{doskoc2021mapping, abstract = {In \emph{inductive inference} we investigate computable devices (learners) learning formal languages. In this work, we focus on \emph{monotonic} learners which, despite their natural motivation, exhibit peculiar behaviour. A recent study analysed the learning capabilities of \emph{strongly monotone} learners in various settings. The therein unveiled differences between \emph{explanatory} (syntactically converging) and \emph{behaviourally correct} (semantically converging) such learners motivate our studies of \emph{monotone} learners in the same settings. While the structure of the pairwise relations for monotone explanatory learning is similar to the strongly monotone case (and for similar reasons), for behaviourally correct learning a very different picture emerges. In the latter setup, we provide a \emph{self-learning} class of languages showing that monotone learners, as opposed to their strongly monotone counterpart, do heavily rely on the order in which the information is given, an unusual result for behaviourally correct learners.}, author = {Doskoč, Vanja and Kötzing, Timo}, booktitle = {Computability in Europe (CiE)}, keywords = {vanjadoskoc timokoetzing year2021 cie}, pages = {146-157}, title = {Mapping Monotonic Restrictions in Inductive Inference}, year = 2021 }

Doskoč, Vanja; Kötzing, Timo Normal Forms for Semantically Witness-Based Learners in Inductive InferenceComputability in Europe (CiE) 2021: 158–168
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In \emph{inductive inference, we study learners (computable devices) inferring formal languages. In particular, we consider \emph{semantically witness-based learners, that is, learners which are required to \emph{justify each of their semantic mind changes. This natural requirement deserves special attention as it is a specialization of various important learning paradigms. As such, it has already proven to be fruitful for gaining knowledge about other types of restrictions. In this paper, we provide a thorough analysis of semantically converging, semantically witness-based learners, obtaining \emph{normal forms for them. Most notably, we show that \emph{set-driven globally semantically witness-based learners are equally powerful as their \emph{Gold-style semantically conservative counterpart. Such results are key to understanding the, yet undiscovered, mutual relation between various important learning paradigms of semantically converging learners.
@inproceedings{doskoc2021normal, abstract = {In \emph{inductive inference}, we study learners (computable devices) inferring formal languages. In particular, we consider \emph{semantically witness-based} learners, that is, learners which are required to \emph{justify} each of their semantic mind changes. This natural requirement deserves special attention as it is a specialization of various important learning paradigms. As such, it has already proven to be fruitful for gaining knowledge about other types of restrictions. In this paper, we provide a thorough analysis of semantically converging, semantically witness-based learners, obtaining \emph{normal forms} for them. Most notably, we show that \emph{set-driven globally} semantically witness-based learners are equally powerful as their \emph{Gold-style semantically conservative} counterpart. Such results are key to understanding the, yet undiscovered, mutual relation between various important learning paradigms of semantically converging learners.}, author = {Doskoč, Vanja and Kötzing, Timo}, booktitle = {Computability in Europe (CiE)}, keywords = {vanjadoskoc timokoetzing year2021 cie}, pages = {158-168}, title = {Normal Forms for Semantically Witness-Based Learners in Inductive Inference}, year = 2021 }

Khazraei, Ardalan; Kötzing, Timo; Seidel, Karen Towards a Map for Incremental Learning in the Limit from Positive and Negative InformationComputability in Europe (CiE) 2021: 273–284
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In order to model an efficient learning paradigm, iterative learning algorithms access data one by one, updating the current hypothesis without regress to past data. Prior research investigating the impact of additional requirements on iterative learners left many questions open, especially in learning from informant, where the input is binary labeled.
@inproceedings{khazraei2021towards, abstract = {In order to model an efficient learning paradigm, iterative learning algorithms access data one by one, updating the current hypothesis without regress to past data. Prior research investigating the impact of additional requirements on iterative learners left many questions open, especially in learning from informant, where the input is binary labeled.}, author = {Khazraei, Ardalan and Kötzing, Timo and Seidel, Karen}, booktitle = {Computability in Europe (CiE)}, keywords = {timokoetzing ardalankhazraei year2021 karenseidel cie}, pages = {273-284}, title = {Towards a Map for Incremental Learning in the Limit from Positive and Negative Information}, year = 2021 }

Kötzing, Timo; Seidel, Karen Learning Languages in the Limit from Positive Information with Finitely Many Memory ChangesComputability in Europe (CiE) 2021: 318–329
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We investigate learning collections of languages from texts by an inductive inference machine with access to the current datum and a bounded memory in form of states. Such a bounded memory states (\(\mathbf{BMS}\)) learner is considered successful in case it eventually settles on a correct hypothesis while exploiting only finitely many different states.
@inproceedings{kotzing2021learning, abstract = {We investigate learning collections of languages from texts by an inductive inference machine with access to the current datum and a bounded memory in form of states. Such a bounded memory states (\(\mathbf{BMS}\)) learner is considered successful in case it eventually settles on a correct hypothesis while exploiting only finitely many different states.}, author = {Kötzing, Timo and Seidel, Karen}, booktitle = {Computability in Europe (CiE)}, keywords = {timokoetzing year2021 karenseidel cie}, pages = {318-329}, title = {Learning Languages in the Limit from Positive Information with Finitely Many Memory Changes}, year = 2021 }

Cohen, Sarel; Hershcovitch, Moshik; Taraz, Martin; Kißig, Otto; Wood, Andrew; Waddington, Daniel; Chin, Peter; Friedrich, Tobias Drug Repurposing using Link Prediction on Knowledge Graphs with Applications to Non-Volatile MemoryComplex Networks and their Applications (ComplexNetworks) 2021: 742–753
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
The active global SARS-CoV-2 pandemic caused more than 167 million cases and 3.4 million deaths worldwide. The development of completely new drugs for such a novel disease is a challenging, time intensive process and despite researchers around the world working on this task, no effective treatments have been developed yet. This emphasizes the importance of \emph{drug repurposing, where treatments are found among existing drugs that are meant for different diseases. A common approach to this is based on \emph{knowledge graphs, that condense relationships between entities like drugs, diseases and genes. Graph neural networks (GNNs) can then be used for the task at hand by predicting links in such knowledge graphs. Expanding on state-of-the-art GNN research, Doshi et al. recently developed the Dr-COVID model. We further extend their work using additional output interpretation strategies. The best aggregation strategy derives a top-100 ranking of candidate drugs, 32 of which currently being in COVID-19-related clinical trials. Moreover, we present an alternative application for the model, the generation of additional candidates based on a given pre-selection of drug candidates using collaborative filtering. In addition, we improved the implementation of the Dr-COVID model by significantly shortening the inference and pre-processing time by exploiting data-parallelism. As drug repurposing is a task that requires high computation and memory resources, we further accelerate the post-processing phase using a new emerging hardware --- we propose a new approach to leverage the use of high-capacity Non-Volatile Memory for aggregate drug ranking.
@inproceedings{cohen2021repurposing, abstract = {The active global SARS-CoV-2 pandemic caused more than 167 million cases and 3.4 million deaths worldwide. The development of completely new drugs for such a novel disease is a challenging, time intensive process and despite researchers around the world working on this task, no effective treatments have been developed yet. This emphasizes the importance of \emph{drug repurposing}, where treatments are found among existing drugs that are meant for different diseases. A common approach to this is based on \emph{knowledge graphs}, that condense relationships between entities like drugs, diseases and genes. Graph neural networks (GNNs) can then be used for the task at hand by predicting links in such knowledge graphs. Expanding on state-of-the-art GNN research, Doshi et al. recently developed the Dr-COVID model. We further extend their work using additional output interpretation strategies. The best aggregation strategy derives a top-100 ranking of candidate drugs, 32 of which currently being in COVID-19-related clinical trials. Moreover, we present an alternative application for the model, the generation of additional candidates based on a given pre-selection of drug candidates using collaborative filtering. In addition, we improved the implementation of the Dr-COVID model by significantly shortening the inference and pre-processing time by exploiting data-parallelism. As drug repurposing is a task that requires high computation and memory resources, we further accelerate the post-processing phase using a new emerging hardware &mdash; we propose a new approach to leverage the use of high-capacity Non-Volatile Memory for aggregate drug ranking.}, author = {Cohen, Sarel and Hershcovitch, Moshik and Taraz, Martin and Kißig, Otto and Wood, Andrew and Waddington, Daniel and Chin, Peter and Friedrich, Tobias}, booktitle = {Complex Networks and their Applications (ComplexNetworks)}, keywords = {sarelcohen ottokissig danielwaddington moshikhershcovitch tobiasfriedrich martintaraz andrewwood complexnetworks peterchin year2021}, pages = {742-753}, title = {Drug Repurposing using Link Prediction on Knowledge Graphs with Applications to Non-Volatile Memory}, year = 2021 }

Bilò, Davide; Cohen, Sarel; Friedrich, Tobias; Schirneck, Martin Near-Optimal Deterministic Single-Source Distance Sensitivity OraclesEuropean Symposium on Algorithms (ESA) 2021: 18:1–18:17
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Given a graph with a distinguished source vertex \(s\), the Single Source Replacement Paths (SSRP) problem is to compute and output, for any target vertex \(t\) and edge \(e\), the length \(d(s,t,e)\) of a shortest path from \(s\) to \(t\) that avoids a failing edge \(e\). A Single-Source Distance Sensitivity Oracle (Single-Source DSO) is a compact data structure that answers queries of the form \((t,e)\) by returning the distance \(d(s,t,e)\). We show how to compress the output of the SSRP problem on \(n\)-vertex, \(m\)-edge graphs with integer edge weights in the range \([1,M]\) into a deterministic Single-Source DSO that has size \(O(M^{1/2 n^{3/2})\) and query time \(\widetildeO(1)\). We prove that the space requirement is optimal (up to the word size). Our techniques can also handle vertex failures within the same bounds. Chechik and Cohen [SODA 2019] presented a combinatorial randomized \(\widetildeO(m\sqrt{n}+n^2)\) time SSRP algorithm for undirected and unweighted graphs. We derandomize their algorithm with the same asymptotic running time and apply our compression to obtain a deterministic Single-Source DSO with \(\widetildeO(m\sqrt{n}+n^2)\) preprocessing time, \(O(n^{3/2})\) space, and \(\widetildeO(1)\) query time. Our combinatorial Single-Source DSO has near-optimal space, preprocessing and query time for dense unweighted graphs, improving the preprocessing time by a \(\sqrt{n}\)-factor compared to previous results. Grandoni and Vassilevska Williams [FOCS 2012, TALG 2020] gave an algebraic randomized \(\widetildeO(Mn^\omega)\) time SSRP algorithm for (undirected and directed) graphs with integer edge weights in the range \([1,M]\), where \(\omega < 2.373\) is the matrix multiplication exponent. We derandomize their algorithm for undirected graphs and apply our compression to obtain an algebraic Single-Source DSO with \(\widetildeO(Mn^\omega)\) preprocessing time, \(O(M^{1/2 n^{3/2})\) space, and \(\widetildeO(1)\) query time. This improves the preprocessing time of algebraic Single-Source DSOs by polynomial factors compared to previous results. We also present further improvements of our Single-Source DSOs. We show that the query time can be reduced to a constant at the cost of increasing the size of the oracle to \(O(M^{1/3 n^{5/3})\) and that all our oracles can be made path-reporting. On sparse graphs with \(m=O(\frac{n^{5/4-\varepsilon}}{M^{7/4}})\) edges, for any constant \(\varepsilon > 0\), we reduce the preprocessing to randomized \(\widetildeO(M^7/8 m^1/2 n^{11/8}) = O(n^{2-\varepsilon/2})\) time. To the best of our knowledge, this is the first truly subquadratic time algorithm for building Single-Source DSOs on sparse graphs.
@inproceedings{bilo2021nearoptimal, abstract = {Given a graph with a distinguished source vertex \(s\), the Single Source Replacement Paths (SSRP) problem is to compute and output, for any target vertex \(t\) and edge \(e\), the length \(d(s,t,e)\) of a shortest path from \(s\) to \(t\) that avoids a failing edge \(e\). A Single-Source Distance Sensitivity Oracle (Single-Source DSO) is a compact data structure that answers queries of the form \((t,e)\) by returning the distance \(d(s,t,e)\). We show how to compress the output of the SSRP problem on \(n\)-vertex, \(m\)-edge graphs with integer edge weights in the range \([1,M]\) into a deterministic Single-Source DSO that has size \(O(M^{1/2} n^{3/2})\) and query time \(\widetilde{O}(1)\). We prove that the space requirement is optimal (up to the word size). Our techniques can also handle vertex failures within the same bounds. Chechik and Cohen [SODA 2019] presented a combinatorial randomized \(\widetilde{O}(m\sqrt{n}+n^2)\) time SSRP algorithm for undirected and unweighted graphs. We derandomize their algorithm with the same asymptotic running time and apply our compression to obtain a deterministic Single-Source DSO with \(\widetilde{O}(m\sqrt{n}+n^2)\) preprocessing time, \(O(n^{3/2})\) space, and \(\widetilde{O}(1)\) query time. Our combinatorial Single-Source DSO has near-optimal space, preprocessing and query time for dense unweighted graphs, improving the preprocessing time by a \(\sqrt{n}\)-factor compared to previous results. Grandoni and Vassilevska Williams [FOCS 2012, TALG 2020] gave an algebraic randomized \(\widetilde{O}(Mn^\omega)\) time SSRP algorithm for (undirected and directed) graphs with integer edge weights in the range \([1,M]\), where \(\omega < 2.373\) is the matrix multiplication exponent. We derandomize their algorithm for undirected graphs and apply our compression to obtain an algebraic Single-Source DSO with \(\widetilde{O}(Mn^\omega)\) preprocessing time, \(O(M^{1/2} n^{3/2})\) space, and \(\widetilde{O}(1)\) query time. This improves the preprocessing time of algebraic Single-Source DSOs by polynomial factors compared to previous results. We also present further improvements of our Single-Source DSOs. We show that the query time can be reduced to a constant at the cost of increasing the size of the oracle to \(O(M^{1/3} n^{5/3})\) and that all our oracles can be made path-reporting. On sparse graphs with \(m=O(\frac{n^{5/4-\varepsilon}}{M^{7/4}})\) edges, for any constant \(\varepsilon > 0\), we reduce the preprocessing to randomized \(\widetilde{O}(M^{7/8} m^{1/2} n^{11/8}) = O(n^{2-\varepsilon/2})\) time. To the best of our knowledge, this is the first truly subquadratic time algorithm for building Single-Source DSOs on sparse graphs.}, author = {Bilò, Davide and Cohen, Sarel and Friedrich, Tobias and Schirneck, Martin}, booktitle = {European Symposium on Algorithms (ESA)}, keywords = {sarelcohen davidebilo esa tobiasfriedrich year2021 martinschirneck}, pages = {18:1&ndash;18:17}, title = {Near-Optimal Deterministic Single-Source Distance Sensitivity Oracles}, year = 2021 }

Bläsius, Thomas; Friedrich, Tobias; Katzmann, Maximilian Efficiently Approximating Vertex Cover on Scale-Free Networks with Underlying Hyperbolic GeometryEuropean Symposium on Algorithms (ESA) 2021: 20:1–20:15
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Finding a minimum vertex cover in a network is a fundamental NP-complete graph problem. One way to deal with its computational hardness, is to trade the qualitative performance of an algorithm (allowing non-optimal outputs) for an improved running time. For the vertex cover problem, there is a gap between theory and practice when it comes to understanding this tradeoff. On the one hand, it is known that it is NP-hard to approximate a minimum vertex cover within a factor of \(\sqrt{2}\). On the other hand, a simple greedy algorithm yields close to optimal approximations in practice. A promising approach towards understanding this discrepancy is to recognize the differences between theoretical worst-case instances and real-world networks. Following this direction, we close the gap between theory and practice by providing an algorithm that efficiently computes nearly optimal vertex cover approximations on hyperbolic random graphs; a network model that closely resembles real-world networks in terms of degree distribution, clustering, and the small-world property. More precisely, our algorithm computes a \((1 + o(1))\)-approximation, asymptotically almost surely, and has a running time of \(\mathcal{O(m \log(n))\). The proposed algorithm is an adaption of the successful greedy approach, enhanced with a procedure that improves on parts of the graph where greedy is not optimal. This makes it possible to introduce a parameter that can be used to tune the tradeoff between approximation performance and running time. Our empirical evaluation on real-world networks shows that this allows for improving over the near-optimal results of the greedy approach.
@inproceedings{blasius2021efficiently, abstract = {Finding a minimum vertex cover in a network is a fundamental NP-complete graph problem. One way to deal with its computational hardness, is to trade the qualitative performance of an algorithm (allowing non-optimal outputs) for an improved running time. For the vertex cover problem, there is a gap between theory and practice when it comes to understanding this tradeoff. On the one hand, it is known that it is NP-hard to approximate a minimum vertex cover within a factor of \(\sqrt{2}\). On the other hand, a simple greedy algorithm yields close to optimal approximations in practice. A promising approach towards understanding this discrepancy is to recognize the differences between theoretical worst-case instances and real-world networks. Following this direction, we close the gap between theory and practice by providing an algorithm that efficiently computes nearly optimal vertex cover approximations on hyperbolic random graphs; a network model that closely resembles real-world networks in terms of degree distribution, clustering, and the small-world property. More precisely, our algorithm computes a \((1 + o(1))\)-approximation, asymptotically almost surely, and has a running time of \(\mathcal{O}(m \log(n))\). The proposed algorithm is an adaption of the successful greedy approach, enhanced with a procedure that improves on parts of the graph where greedy is not optimal. This makes it possible to introduce a parameter that can be used to tune the tradeoff between approximation performance and running time. Our empirical evaluation on real-world networks shows that this allows for improving over the near-optimal results of the greedy approach.}, author = {Bläsius, Thomas and Friedrich, Tobias and Katzmann, Maximilian}, booktitle = {European Symposium on Algorithms (ESA)}, keywords = {esa thomasblaesius tobiasfriedrich maximiliankatzmann year2021}, pages = {20:1-20:15}, title = {Efficiently Approximating Vertex Cover on Scale-Free Networks with Underlying Hyperbolic Geometry}, year = 2021 }

Bläsius, Thomas; Friedrich, Tobias; Weyand, Christopher Efficiently Computing Maximum Flows in Scale-Free NetworksEuropean Symposium on Algorithms (ESA) 2021: 21:1–21:14
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We study the maximum-flow/minimum-cut problem on scale-free networks, i.e., graphs whose degree distribution follows a power-law. We propose a simple algorithm that capitalizes on the fact that often only a small fraction of such a network is relevant for the flow. At its core, our algorithm augments Dinitz's algorithm with a balanced bidirectional search. Our experiments on a scale-free random network model indicate sublinear run time. On scale-free real-world networks, we outperform the commonly used highest-label Push-Relabel implementation by up to two orders of magnitude. Compared to Dinitz's original algorithm, our modifications reduce the search space, e.g., by a factor of 275 on an autonomous systems graph. Beyond these good run times, our algorithm has an additional advantage compared to Push-Relabel. The latter computes a preflow, which makes the extraction of a minimum cut potentially more difficult. This is relevant, for example, for the computation of Gomory-Hu trees. On a social network with 70000 nodes, our algorithm computes the Gomory-Hu tree in 3 seconds compared to 12 minutes when using Push-Relabel.
@inproceedings{blasius2021efficiently, abstract = {We study the maximum-flow/minimum-cut problem on scale-free networks, i.e., graphs whose degree distribution follows a power-law. We propose a simple algorithm that capitalizes on the fact that often only a small fraction of such a network is relevant for the flow. At its core, our algorithm augments Dinitz's algorithm with a balanced bidirectional search. Our experiments on a scale-free random network model indicate sublinear run time. On scale-free real-world networks, we outperform the commonly used highest-label Push-Relabel implementation by up to two orders of magnitude. Compared to Dinitz's original algorithm, our modifications reduce the search space, e.g., by a factor of 275 on an autonomous systems graph. Beyond these good run times, our algorithm has an additional advantage compared to Push-Relabel. The latter computes a preflow, which makes the extraction of a minimum cut potentially more difficult. This is relevant, for example, for the computation of Gomory-Hu trees. On a social network with 70000 nodes, our algorithm computes the Gomory-Hu tree in 3 seconds compared to 12 minutes when using Push-Relabel.}, author = {Bläsius, Thomas and Friedrich, Tobias and Weyand, Christopher}, booktitle = {European Symposium on Algorithms (ESA)}, keywords = {esa thomasblaesius tobiasfriedrich christopherweyand year2021}, pages = {21:1-21:14}, title = {Efficiently Computing Maximum Flows in Scale-Free Networks}, year = 2021 }

Casel, Katrin; Friedrich, Tobias; Issac, Davis; Niklanovits, Aikaterini; Zeif, Ziena Balanced Crown Decomposition for Connectivity ConstraintsEuropean Symposium on Algorithms (ESA) 2021: 26:1–26:15
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We introduce the balanced crown decomposition that captures the structure imposed on graphs by their connected induced subgraphs of a given size. Such subgraphs are a popular modeling tool in various application areas, where the non-local nature of the connectivity condition usually results in very challenging algorithmic tasks. The balanced crown decomposition is a combination of a crown decomposition and a balanced partition which makes it applicable to graph editing as well as graph packing and partitioning problems. We illustrate this by deriving improved approximation algorithms and kernelization for a variety of such problems. In particular, through this structure, we obtain the first constant-factor approximation for the Balanced Connected Partition (BCP) problem, where the task is to partition a vertex-weighted graph into k connected components of approximately equal weight. We derive a \(3\)-approximation for the two most commonly used objectives of maximizing the weight of the lightest component or minimizing the weight of the heaviest component.
@inproceedings{casel2021balanced, abstract = {We introduce the balanced crown decomposition that captures the structure imposed on graphs by their connected induced subgraphs of a given size. Such subgraphs are a popular modeling tool in various application areas, where the non-local nature of the connectivity condition usually results in very challenging algorithmic tasks. The balanced crown decomposition is a combination of a crown decomposition and a balanced partition which makes it applicable to graph editing as well as graph packing and partitioning problems. We illustrate this by deriving improved approximation algorithms and kernelization for a variety of such problems. In particular, through this structure, we obtain the first constant-factor approximation for the Balanced Connected Partition (BCP) problem, where the task is to partition a vertex-weighted graph into k connected components of approximately equal weight. We derive a \(3\)-approximation for the two most commonly used objectives of maximizing the weight of the lightest component or minimizing the weight of the heaviest component.}, author = {Casel, Katrin and Friedrich, Tobias and Issac, Davis and Niklanovits, Aikaterini and Zeif, Ziena}, booktitle = {European Symposium on Algorithms (ESA)}, keywords = {sys:relevantfor:ae zienazeif esa katrincasel davisissac aikaterininiklanovits tobiasfriedrich year2021}, pages = {26:1&ndash;26:15}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {Balanced Crown Decomposition for Connectivity Constraints}, volume = 204, year = 2021 }

Behrendt, Lukas; Casel, Katrin; Friedrich, Tobias; Lagodzinski, J. A. Gregor; Löser, Alexander; Wilhelm, Marcus From Symmetry to Asymmetry: Generalizing TSP Approximations by ParametrizationFundamentals of Computation Theory (FCT) 2021: 53–66
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We generalize the tree doubling and Christofides algorithm to parameterized approximations for ATSP. The parameters we consider for the respective generalizations are upper bounded by the number of asymmetric distances, which yields algorithms to efficiently compute good approximations also for moderately asymmetric TSP instances. As generalization of the Christofides algorithm, we derive a parameterized 2.5-approximation, where the parameter is the size of a vertex cover for the subgraph induced by the asymmetric distances. Our generalization of the tree doubling algorithm gives a parameterized 3-approximation, where the parameter is the minimum number of asymmetric distances in a minimum spanning arborescence. Further, we combine these with a notion of symmetry relaxation which allows to trade approximation guarantee for runtime. Since the two parameters we consider are theoretically incomparable, we present experimental results which show that generalized tree doubling frequently outperforms generalized Christofides with respect to parameter size.
@inproceedings{behrendt2021symmetry, abstract = {We generalize the tree doubling and Christofides algorithm to parameterized approximations for ATSP. The parameters we consider for the respective generalizations are upper bounded by the number of asymmetric distances, which yields algorithms to efficiently compute good approximations also for moderately asymmetric TSP instances. As generalization of the Christofides algorithm, we derive a parameterized 2.5-approximation, where the parameter is the size of a vertex cover for the subgraph induced by the asymmetric distances. Our generalization of the tree doubling algorithm gives a parameterized 3-approximation, where the parameter is the minimum number of asymmetric distances in a minimum spanning arborescence. Further, we combine these with a notion of symmetry relaxation which allows to trade approximation guarantee for runtime. Since the two parameters we consider are theoretically incomparable, we present experimental results which show that generalized tree doubling frequently outperforms generalized Christofides with respect to parameter size.}, author = {Behrendt, Lukas and Casel, Katrin and Friedrich, Tobias and Lagodzinski, J. A. Gregor and Löser, Alexander and Wilhelm, Marcus}, booktitle = {Fundamentals of Computation Theory (FCT)}, editor = {Bampis, Evripidis and Pagourtzis, Aris}, keywords = {gregorlagodzinski alexanderloeser lukasbehrend katrincasel fct tobiasfriedrich year2021 marcuswilhelm}, pages = {53&ndash;66}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {From Symmetry to Asymmetry: Generalizing {TSP} Approximations by Parametrization}, volume = 12867, year = 2021 }

Berger, Julian; Bleidt, Tibor; Büßemeyer, Martin; Ding, Marcus; Feldmann, Moritz; Feuerpfeil, Moritz; Jacoby, Janusch; Schröter, Valentin; Sievers, Bjarne; Spranger, Moritz; Stadlinger, Simon; Wullenweber, Paul; Cohen, Sarel; Doskoč, Vanja; Friedrich, Tobias Fine-Grained Localization, Classification and Segmentation of Lungs with Various DiseasesCVPR Workshop on Fine-Grained Visual Categorization (FGVC@CVPR) 2021
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The fine-grained localization and classification of various lung abnormalities is a challenging yet important task for combating diseases and, also, pandemics. In this paper, we present one way to detect and classify abnormalities within chest X-ray scans. In particular, we investigate the use of binary image classification (to distinguish between healthy and infected chests) and the weighted box fusion (which constructs a detection box using the proposed boxes within range). We observe that both methods increase the performance of a base model significantly. Furthermore, we improve state of the art on lung segmentation, even in the presence of abnormalities. We do so using transfer learning to fine-tune a UNet model on the Montgomery and Shenzhen datasets. In our experiments, we compare standard augmentations (like crop, pad, rotate, warp, zoom, brightness, and contrast variations) to more complex ones (for example, block masking and diffused noise augmentations). This way, we obtain a state-of-the-art model with a dice score of 97.9%. In particular, we show that simple augmentations outperform complex ones in our setting.
@inproceedings{berger2021finegrained, abstract = {The fine-grained localization and classification of various lung abnormalities is a challenging yet important task for combating diseases and, also, pandemics. In this paper, we present one way to detect and classify abnormalities within chest X-ray scans. In particular, we investigate the use of binary image classification (to distinguish between healthy and infected chests) and the weighted box fusion (which constructs a detection box using the proposed boxes within range). We observe that both methods increase the performance of a base model significantly. Furthermore, we improve state of the art on lung segmentation, even in the presence of abnormalities. We do so using transfer learning to fine-tune a UNet model on the Montgomery and Shenzhen datasets. In our experiments, we compare standard augmentations (like crop, pad, rotate, warp, zoom, brightness, and contrast variations) to more complex ones (for example, block masking and diffused noise augmentations). This way, we obtain a state-of-the-art model with a dice score of 97.9\%. In particular, we show that simple augmentations outperform complex ones in our setting.}, author = {Berger, Julian and Bleidt, Tibor and Büßemeyer, Martin and Ding, Marcus and Feldmann, Moritz and Feuerpfeil, Moritz and Jacoby, Janusch and Schröter, Valentin and Sievers, Bjarne and Spranger, Moritz and Stadlinger, Simon and Wullenweber, Paul and Cohen, Sarel and Doskoč, Vanja and Friedrich, Tobias}, booktitle = {CVPR Workshop on Fine-Grained Visual Categorization (FGVC@CVPR)}, keywords = {sarelcohen vanjadoskoc martinbuessemeyer fgvc@cvpr tobiasfriedrich marcusding moritzfeuerpfeil paulwullenweber moritzspranger moritzfeldmann januschjacoby tiborbleidt valentinschroeter simonstadlinger julianberger year2021 bjarnesievers}, title = {Fine-Grained Localization, Classification and Segmentation of Lungs with Various Diseases}, year = 2021 }

Böther, Maximilian; Schiller, Leon; Fischbeck, Philipp; Molitor, Louise; Krejca, Martin S.; Friedrich, Tobias Evolutionary Minimization of Traffic CongestionGenetic and Evolutionary Computation Conference (GECCO) 2021: 937–945
Best-Paper Award (RWA Track)
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Traffic congestion is a major issue that can be solved by suggesting drivers alternative routes they are willing to take. This concept has been formalized as a strategic routing problem in which a single alternative route is suggested to an existing one. We extend this formalization and introduce the Multiple-Routes problem, which is given a start and a destination and then aims at finding up to \(n\) different routes that the drivers strategically disperse over, minimizing the overall travel time of the system. Due to the NP-hard nature of the problem, we introduce the Multiple-Routes evolutionary algorithm (MREA) as a heuristic solver. We study several mutation and crossover operators and evaluate them on real-world data of the city of Berlin, Germany. We find that a combination of all operators yields the best result, improving the overall travel time by a factor between 1.8 and 3, in the median, compared to all drivers taking the fastest route. For the base case \(n=2\), we compare our MREA to the highly tailored optimal solver by Bläsius etal. [ATMOS 2020] and show that, in the median, our approach finds solutions of quality at least \(99.69\%\) of an optimal solution while only requiring \(40\%\) of the time.
@inproceedings{boether2021evolutionary, abstract = {Traffic congestion is a major issue that can be solved by suggesting drivers alternative routes they are willing to take. This concept has been formalized as a strategic routing problem in which a single alternative route is suggested to an existing one. We extend this formalization and introduce the Multiple-Routes problem, which is given a start and a destination and then aims at finding up to \(n\) different routes that the drivers strategically disperse over, minimizing the overall travel time of the system. Due to the NP-hard nature of the problem, we introduce the Multiple-Routes evolutionary algorithm (MREA) as a heuristic solver. We study several mutation and crossover operators and evaluate them on real-world data of the city of Berlin, Germany. We find that a combination of all operators yields the best result, improving the overall travel time by a factor between 1.8 and 3, in the median, compared to all drivers taking the fastest route. For the base case \(n=2\), we compare our MREA to the highly tailored optimal solver by Bläsius etal. [ATMOS 2020] and show that, in the median, our approach finds solutions of quality at least \(99.69\%\) of an optimal solution while only requiring \(40\%\) of the time.}, author = {Böther, Maximilian and Schiller, Leon and Fischbeck, Philipp and Molitor, Louise and Krejca, Martin S. and Friedrich, Tobias}, booktitle = {Genetic and Evolutionary Computation Conference (GECCO)}, keywords = {maximilianboether philippfischbeck louisemolitor martinskrejca tobiasfriedrich gecco leonschiller year2021}, note = {Best-Paper Award (RWA Track)}, pages = {937&ndash;945}, title = {Evolutionary Minimization of Traffic Congestion}, year = 2021 }

Doerr, Benjamin; Kötzing, Timo Lower Bounds from Fitness Levels Made EasyGenetic and Evolutionary Computation Conference (GECCO) 2021: 1142–1150
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One of the first and easy to use techniques for proving run time bounds for evolutionary algorithms is the so-called method of fitness levels by Wegener. It uses a partition of the search space into a sequence of levels which are traversed by the algorithm in increasing order, possibly skipping levels. An easy, but often strong upper bound for the run time can then be derived by adding the reciprocals of the probabilities to leave the levels (or upper bounds for these). Unfortunately, a similarly effective method for proving lower bounds has not yet been established. The strongest such method, proposed by Sudholt (2013), requires a careful choice of the viscosity parameters gamma. In this paper we present two new variants of the method, one for upper and one for lower bounds. Besides the level leaving probabilities, they only rely on the probabilities that levels are visited at all. We show that these can be computed or estimated without greater difficulties and apply our method to reprove the following known results in an easy and natural way. (i) The precise run time of the (1+1) EA on LeadingOnes. (ii) A lower bound for the run time of the (1+1) EA on OneMax, tight apart from an O(n) term. (iii) A lower bound for the run time of the (1+1) EA on long k-paths.
@inproceedings{doerr2021lower, abstract = {One of the first and easy to use techniques for proving run time bounds for evolutionary algorithms is the so-called method of fitness levels by Wegener. It uses a partition of the search space into a sequence of levels which are traversed by the algorithm in increasing order, possibly skipping levels. An easy, but often strong upper bound for the run time can then be derived by adding the reciprocals of the probabilities to leave the levels (or upper bounds for these). Unfortunately, a similarly effective method for proving lower bounds has not yet been established. The strongest such method, proposed by Sudholt (2013), requires a careful choice of the viscosity parameters gamma. In this paper we present two new variants of the method, one for upper and one for lower bounds. Besides the level leaving probabilities, they only rely on the probabilities that levels are visited at all. We show that these can be computed or estimated without greater difficulties and apply our method to reprove the following known results in an easy and natural way. (i) The precise run time of the (1+1) EA on LeadingOnes. (ii) A lower bound for the run time of the (1+1) EA on OneMax, tight apart from an O(n) term. (iii) A lower bound for the run time of the (1+1) EA on long k-paths.}, author = {Doerr, Benjamin and Kötzing, Timo}, booktitle = {Genetic and Evolutionary Computation Conference (GECCO)}, keywords = {timokoetzing benjamindoerr gecco year2021}, pages = {1142-1150}, title = {Lower Bounds from Fitness Levels Made Easy}, year = 2021 }

Wood, Andrew; Hershcovitch, Moshik; Waddington, Daniel; Cohen, Sarel; Chin, Peter Non-Volatile Memory Accelerated Posterior EstimationHigh Performance and Embedded Computing (HPEC) 2021
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Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their predictions are wrong. To use more learnable parameter combinations efficiently, these samples must be drawn from the posterior distribution. Unfortunately computing the posterior directly is infeasible, so often researchers approximate it with a well known distribution such as a Gaussian. In this paper, we show that through the use of high-capacity persistent storage, models whose posterior distribution was too big to approximate are now feasible, leading to improved predictions in downstream tasks.
@inproceedings{wood2021nonvolatile, abstract = {Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their predictions are wrong. To use more learnable parameter combinations efficiently, these samples must be drawn from the posterior distribution. Unfortunately computing the posterior directly is infeasible, so often researchers approximate it with a well known distribution such as a Gaussian. In this paper, we show that through the use of high-capacity persistent storage, models whose posterior distribution was too big to approximate are now feasible, leading to improved predictions in downstream tasks.}, author = {Wood, Andrew and Hershcovitch, Moshik and Waddington, Daniel and Cohen, Sarel and Chin, Peter}, booktitle = {High Performance and Embedded Computing (HPEC)}, keywords = {sarelcohen danielwaddington hpec moshikhershcovitch andrewwood peterchin year2021}, title = {Non-Volatile Memory Accelerated Posterior Estimation}, year = 2021 }

Wood, Andrew; Hershcovitch, Moshik; Waddington, Daniel; Cohen, Sarel; Wolf, Meredith; Suh, Hongjun; Zong, Weiyu; Chin, Peter Non-Volatile Memory Accelerated Geometric Multi-Scale Resolution AnalysisHigh Performance and Embedded Computing (HPEC) 2021: 1–7
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Dimensionality reduction algorithms are standard tools in a researcher's toolbox. Dimensionality reduction algorithms are frequently used to augment downstream tasks such as machine learning, data science, and also are exploratory methods for understanding complex phenomena. For instance, dimensionality reduction is commonly used in Biology as well as Neuroscience to understand data collected from biological subjects. However, dimensionality reduction techniques are limited by the von-Neumann architectures that they execute on. Specifically, data intensive algorithms such as dimensionality reduction techniques often require fast, high capacity, persistent memory which historically hardware has been unable to provide at the same time. In this paper, we present a re-implementation of an existing dimensionality reduction technique called Geometric Multi-Scale Resolution Analysis (GMRA) which has been accelerated via novel persistent memory technology called Memory Centric Active Storage (MCAS). Our implementation uses a specialized version of MCAS called PyMM that provides native support for Python datatypes including NumPy arrays and PyTorch tensors. We compare our PyMM implementation against a DRAM implementation, and show that when data fits in DRAM, PyMM offers competitive runtimes. When data does not fit in DRAM, our PyMM implementation is still able to process the data.
@inproceedings{wood2021nonvolatile, abstract = {Dimensionality reduction algorithms are standard tools in a researcher's toolbox. Dimensionality reduction algorithms are frequently used to augment downstream tasks such as machine learning, data science, and also are exploratory methods for understanding complex phenomena. For instance, dimensionality reduction is commonly used in Biology as well as Neuroscience to understand data collected from biological subjects. However, dimensionality reduction techniques are limited by the von-Neumann architectures that they execute on. Specifically, data intensive algorithms such as dimensionality reduction techniques often require fast, high capacity, persistent memory which historically hardware has been unable to provide at the same time. In this paper, we present a re-implementation of an existing dimensionality reduction technique called Geometric Multi-Scale Resolution Analysis (GMRA) which has been accelerated via novel persistent memory technology called Memory Centric Active Storage (MCAS). Our implementation uses a specialized version of MCAS called PyMM that provides native support for Python datatypes including NumPy arrays and PyTorch tensors. We compare our PyMM implementation against a DRAM implementation, and show that when data fits in DRAM, PyMM offers competitive runtimes. When data does not fit in DRAM, our PyMM implementation is still able to process the data.}, author = {Wood, Andrew and Hershcovitch, Moshik and Waddington, Daniel and Cohen, Sarel and Wolf, Meredith and Suh, Hongjun and Zong, Weiyu and Chin, Peter}, booktitle = {High Performance and Embedded Computing (HPEC)}, keywords = {sarelcohen danielwaddington hpec moshikhershcovitch hongjunsuh weiyuzong andrewwood meredithwolf peterchin year2021}, pages = {1-7}, title = {Non-Volatile Memory Accelerated Geometric Multi-Scale Resolution Analysis}, year = 2021 }

Friedrich, Tobias; Göbel, Andreas; Krejca, Martin S.; Pappik, Marcus A spectral independence view on hard spheres via block dynamicsInternational Colloquium on Automata, Languages and Programming (ICALP) 2021: 66:1–66:15
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The hard-sphere model is one of the most extensively studied models in statistical physics. It describes the continuous distribution of spherical particles, governed by hard-core interactions. An important quantity of this model is the normalizing factor of this distribution, called the partition function. We propose a Markov chain Monte Carlo algorithm for approximating the grand-canonical partition function of the hard-sphere model in \(d\) dimensions. Up to a fugacity of \( \lambda < \text{e}/2^d\), the runtime of our algorithm is polynomial in the volume of the system. This covers the entire known real-valued regime for the uniqueness of the Gibbs measure. Key to our approach is to define a discretization that closely approximates the partition function of the continuous model. This results in a discrete hard-core instance that is exponential in the size of the initial hard-sphere model. Our approximation bound follows directly from the correlation decay threshold of an infinite regular tree with degree equal to the maximum degree of our discretization. To cope with the exponential blow-up of the discrete instance we use clique dynamics, a Markov chain that was recently introduced in the setting of abstract polymer models. We prove rapid mixing of clique dynamics up to the tree threshold of the univariate hard-core model. This is achieved by relating clique dynamics to block dynamics and adapting the spectral expansion method, which was recently used to bound the mixing time of Glauber dynamics within the same parameter regime.
@inproceedings{fgkp-asivohsvbd-2021, abstract = {The hard-sphere model is one of the most extensively studied models in statistical physics. It describes the continuous distribution of spherical particles, governed by hard-core interactions. An important quantity of this model is the normalizing factor of this distribution, called the partition function. We propose a Markov chain Monte Carlo algorithm for approximating the grand-canonical partition function of the hard-sphere model in \(d\) dimensions. Up to a fugacity of \( \lambda < \text{e}/2^d\), the runtime of our algorithm is polynomial in the volume of the system. This covers the entire known real-valued regime for the uniqueness of the Gibbs measure. Key to our approach is to define a discretization that closely approximates the partition function of the continuous model. This results in a discrete hard-core instance that is exponential in the size of the initial hard-sphere model. Our approximation bound follows directly from the correlation decay threshold of an infinite regular tree with degree equal to the maximum degree of our discretization. To cope with the exponential blow-up of the discrete instance we use clique dynamics, a Markov chain that was recently introduced in the setting of abstract polymer models. We prove rapid mixing of clique dynamics up to the tree threshold of the univariate hard-core model. This is achieved by relating clique dynamics to block dynamics and adapting the spectral expansion method, which was recently used to bound the mixing time of Glauber dynamics within the same parameter regime.}, author = {Friedrich, Tobias and Göbel, Andreas and Krejca, Martin S. and Pappik, Marcus}, booktitle = {International Colloquium on Automata, Languages and Programming (ICALP)}, keywords = {marcuspappik martinskrejca andreasgoebel tobiasfriedrich icalp year2021}, pages = {66:1-66:15}, title = {A spectral independence view on hard spheres via block dynamics}, volume = 198, year = 2021 }

Lagodzinski, J. A. Gregor; Göbel, Andreas; Casel, Katrin; Friedrich, Tobias On Counting (Quantum-)Graph Homomorphisms in Finite Fields of Prime OrderInternational Colloquium on Automata, Languages and Programming (ICALP) 2021: 91:1–91:15
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
We study the problem of counting the number of homomorphisms from an input graph \(G\) to a fixed (quantum) graph \(\bar{H}\) in any finite field of prime order \(\mathbb{Z}_p\). The subproblem with graph \(H\) was introduced by Faben and Jerrum [ToC'15] and its complexity is still uncharacterised despite active research, e.g. the very recent work of Focke, Goldberg, Roth, and Zivný [SODA'21]. Our contribution is threefold. First, we introduce the study of quantum graphs to the study of modular counting homomorphisms. We show that the complexity for a quantum graph \(\bar{H}\) collapses to the complexity criteria found at dimension 1: graphs. Second, in order to prove cases of intractability we establish a further reduction to the study of bipartite graphs. Lastly, we establish a dichotomy for all bipartite \( (K_3,3 \ e, domino) \)-free graphs by a thorough structural study incorporating both local and global arguments. This result subsumes all results on bipartite graphs known for all prime moduli and extends them significantly. Even for the subproblem with \(p=2\) this establishes new results.
@inproceedings{lagodzinski2021counting, abstract = {We study the problem of counting the number of homomorphisms from an input graph \(G\) to a fixed (quantum) graph \(\bar{H}\) in any finite field of prime order \(\mathbb{Z}_p\). The subproblem with graph \(H\) was introduced by Faben and Jerrum [ToC'15] and its complexity is still uncharacterised despite active research, e.g. the very recent work of Focke, Goldberg, Roth, and Zivný [SODA'21]. Our contribution is threefold. First, we introduce the study of quantum graphs to the study of modular counting homomorphisms. We show that the complexity for a quantum graph \(\bar{H}\) collapses to the complexity criteria found at dimension 1: graphs. Second, in order to prove cases of intractability we establish a further reduction to the study of bipartite graphs. Lastly, we establish a dichotomy for all bipartite \( (K_{3,3} \ {e}, domino) \)-free graphs by a thorough structural study incorporating both local and global arguments. This result subsumes all results on bipartite graphs known for all prime moduli and extends them significantly. Even for the subproblem with \(p=2\) this establishes new results.}, author = {Lagodzinski, J. A. Gregor and Göbel, Andreas and Casel, Katrin and Friedrich, Tobias}, booktitle = {International Colloquium on Automata, Languages and Programming (ICALP)}, editor = {Bansal, Nikhil and Merelli, Emanuela and Worrell, James}, keywords = {gregorlagodzinski katrincasel andreasgoebel tobiasfriedrich icalp year2021}, pages = {91:1&ndash;91:15}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum f{{ü}}r Informatik}, series = {LIPIcs}, title = {On Counting (Quantum-)Graph Homomorphisms in Finite Fields of Prime Order}, volume = 198, year = 2021 }

Casel, Katrin; Schmid, Markus L. Fine-Grained Complexity of Regular Path QueriesInternational Conference on Database Theory (ICDT) 2021: 19:1–19:20
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
A regular path query (RPQ) is a regular expression \(q\) that returns all node pairs \((u, v)\) from a graph database that are connected by an arbitrary path labelled with a word from \(L(q)\). The obvious algorithmic approach to RPQ-evaluation (called PG-approach), i.e., constructing the product graph between an NFA for \(q\) and the graph database, is appealing due to its simplicity and also leads to efficient algorithms. However, it is unclear whether the PG-approach is optimal. We address this question by thoroughly investigating which upper complexity bounds can be achieved by the PG-approach, and we complement these with conditional lower bounds (in the sense of the fine-grained complexity framework). A special focus is put on enumeration and delay bounds, as well as the data complexity perspective. A main insight is that we can achieve optimal (or near optimal) algorithms with the PG-approach, but the delay for enumeration is rather high (linear in the database). We explore three successful approaches towards enumeration with sub-linear delay: super-linear preprocessing, approximations of the solution sets, and restricted classes of RPQs.
@inproceedings{casel2021finegrained, abstract = {A regular path query (RPQ) is a regular expression \(q\) that returns all node pairs \((u, v)\) from a graph database that are connected by an arbitrary path labelled with a word from \(L(q)\). The obvious algorithmic approach to RPQ-evaluation (called PG-approach), i.e., constructing the product graph between an NFA for \(q\) and the graph database, is appealing due to its simplicity and also leads to efficient algorithms. However, it is unclear whether the PG-approach is optimal. We address this question by thoroughly investigating which upper complexity bounds can be achieved by the PG-approach, and we complement these with conditional lower bounds (in the sense of the fine-grained complexity framework). A special focus is put on enumeration and delay bounds, as well as the data complexity perspective. A main insight is that we can achieve optimal (or near optimal) algorithms with the PG-approach, but the delay for enumeration is rather high (linear in the database). We explore three successful approaches towards enumeration with sub-linear delay: super-linear preprocessing, approximations of the solution sets, and restricted classes of RPQs.}, author = {Casel, Katrin and Schmid, Markus L.}, booktitle = {International Conference on Database Theory (ICDT)}, keywords = {markuslschmid katrincasel icdt year2021}, pages = {19:1-19:20}, title = {Fine-Grained Complexity of Regular Path Queries}, year = 2021 }

Krogmann, Simon; Lenzner, Pascal; Molitor, Louise; Skopalik, Alexander Two-Stage Facility Location Games with Strategic Clients and FacilitiesInternational Joint Conference on Artificial Intelligence (IJCAI) 2021: 292–298
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
We consider non-cooperative facility location games where both facilities and clients act strategically and heavily influence each other. This contrasts established game-theoretic facility location models with non-strategic clients that simply select the closest opened facility. In our model, every facility location has a set of attracted clients and each client has a set of shopping locations and a weight that corresponds to her spending capacity. Facility agents selfishly select a location for opening their facility to maximize the attracted total spending capacity, whereas clients strategically decide how to distribute their spending capacity among the opened facilities in their shopping range. We focus on a natural client behavior similar to classical load balancing: our selfish clients aim for a distribution that minimizes their maximum waiting times for getting serviced, where a facility’s waiting time corresponds to its total attracted client weight. We show that subgame perfect equilibria exist and give almost tight constant bounds on the Price of Anarchy and the Price of Stability, which even hold for a broader class of games with arbitrary client behavior. Since facilities and clients influence each other, it is crucial for the facilities to anticipate the selfish clients’ behavior when selecting their location. For this, we provide an efficient algorithm that also implies an efficient check for equilibrium. Finally, we show that computing a socially optimal facility placement is NP-hard and that this result holds for all feasible client weight distributions.
@inproceedings{krogmann2021twostage, abstract = {We consider non-cooperative facility location games where both facilities and clients act strategically and heavily influence each other. This contrasts established game-theoretic facility location models with non-strategic clients that simply select the closest opened facility. In our model, every facility location has a set of attracted clients and each client has a set of shopping locations and a weight that corresponds to her spending capacity. Facility agents selfishly select a location for opening their facility to maximize the attracted total spending capacity, whereas clients strategically decide how to distribute their spending capacity among the opened facilities in their shopping range. We focus on a natural client behavior similar to classical load balancing: our selfish clients aim for a distribution that minimizes their maximum waiting times for getting serviced, where a facility’s waiting time corresponds to its total attracted client weight. We show that subgame perfect equilibria exist and give almost tight constant bounds on the Price of Anarchy and the Price of Stability, which even hold for a broader class of games with arbitrary client behavior. Since facilities and clients influence each other, it is crucial for the facilities to anticipate the selfish clients’ behavior when selecting their location. For this, we provide an efficient algorithm that also implies an efficient check for equilibrium. Finally, we show that computing a socially optimal facility placement is NP-hard and that this result holds for all feasible client weight distributions.}, author = {Krogmann, Simon and Lenzner, Pascal and Molitor, Louise and Skopalik, Alexander}, booktitle = {International Joint Conference on Artificial Intelligence (IJCAI)}, keywords = {ijcai louisemolitor simonkrogmann pascallenzner year2021}, pages = {292-298}, title = {Two-Stage Facility Location Games with Strategic Clients and Facilities}, year = 2021 }

Bläsius, Thomas; Fischbeck, Philipp; Gottesbüren, Lars; Hamann, Michael; Heuer, Tobias; Spinner, Jonas; Weyand, Christopher; Wilhelm, Marcus PACE Solver Description: The KaPoCE Exact Cluster Editing AlgorithmInternational Symposium on Parameterized and Exact Computation (IPEC) 2021: 27:1–27:3
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The cluster editing problem is to transform an input graph into a cluster graph by performing a minimum number of edge editing operations. A cluster graph is a graph where each connected component is a clique. An edit operation can be either adding a new edge or removing an existing edge. In this write-up we outline the core techniques used in the exact cluster editing algorithm of the KaPoCE framework (contains also a heuristic solver), submitted to the exact track of the 2021 PACE challenge.
@inproceedings{blaesius2021exact, abstract = {The cluster editing problem is to transform an input graph into a cluster graph by performing a minimum number of edge editing operations. A cluster graph is a graph where each connected component is a clique. An edit operation can be either adding a new edge or removing an existing edge. In this write-up we outline the core techniques used in the exact cluster editing algorithm of the KaPoCE framework (contains also a heuristic solver), submitted to the exact track of the 2021 PACE challenge.}, author = {Bläsius, Thomas and Fischbeck, Philipp and Gottesbüren, Lars and Hamann, Michael and Heuer, Tobias and Spinner, Jonas and Weyand, Christopher and Wilhelm, Marcus}, booktitle = {International Symposium on Parameterized and Exact Computation (IPEC)}, keywords = {philippfischbeck larsgottesbueren thomasblaesius ipec michaelhamann tobiasheuer christopherweyand year2021 marcuswilhelm jonasspinner}, pages = {27:1&ndash;27:3}, title = {PACE Solver Description: The KaPoCE Exact Cluster Editing Algorithm}, year = 2021 }

Bläsius, Thomas; Fischbeck, Philipp; Gottesbüren, Lars; Hamann, Michael; Heuer, Tobias; Spinner, Jonas; Weyand, Christopher; Wilhelm, Marcus PACE Solver Description: KaPoCE: A Heuristic Cluster Editing AlgorithmInternational Symposium on Parameterized and Exact Computation (IPEC) 2021: 31:1–31:4
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
The cluster editing problem is to transform an input graph into a cluster graph by performing a minimum number of edge editing operations. A cluster graph is a graph where each connected component is a clique. An edit operation can be either adding a new edge or removing an existing edge. In this write-up we outline the core techniques used in the heuristic cluster editing algorithm of the Karlsruhe and Potsdam Cluster Editing (KaPoCE) framework, submitted to the heuristic track of the 2021 PACE challenge.
@inproceedings{blaesius2021heuristic, abstract = {The cluster editing problem is to transform an input graph into a cluster graph by performing a minimum number of edge editing operations. A cluster graph is a graph where each connected component is a clique. An edit operation can be either adding a new edge or removing an existing edge. In this write-up we outline the core techniques used in the heuristic cluster editing algorithm of the Karlsruhe and Potsdam Cluster Editing (KaPoCE) framework, submitted to the heuristic track of the 2021 PACE challenge.}, author = {Bläsius, Thomas and Fischbeck, Philipp and Gottesbüren, Lars and Hamann, Michael and Heuer, Tobias and Spinner, Jonas and Weyand, Christopher and Wilhelm, Marcus}, booktitle = {International Symposium on Parameterized and Exact Computation (IPEC)}, keywords = {philippfischbeck larsgottesbueren thomasblaesius ipec michaelhamann tobiasheuer christopherweyand year2021 marcuswilhelm jonasspinner}, pages = {31:1&ndash;31:4}, title = {PACE Solver Description: KaPoCE: A Heuristic Cluster Editing Algorithm}, year = 2021 }

Bläsius, Thomas; Friedrich, Tobias; Krejca, Martin S.; Molitor, Louise The Impact of Geometry on Monochrome Regions in the Flip Schelling ProcessInternational Symposium on Algorithms and Computation, (ISAAC) 2021 2021: 29:1–29:17
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Schelling’s classical segregation model gives a coherent explanation for the wide-spread phenomenon of residential segregation. We consider an agent-based saturated open-city variant, the Flip-Schelling-Process (FSP), in which agents, placed on a graph, have one out of two types and, based on the predominant type in their neighborhood, decide whether to changes their types; similar to a new agent arriving as soon as another agent leaves the vertex. We investigate the probability that an edge u,vis monochrome, i.e., that both vertices u and v have the same type in the FSP, and we provide a general framework for analyzing the influence of the underlying graph topology on residential segregation. In particular, for two adjacent vertices, we show that a highly decisive common neighborhood, i.e., a common neighborhood where the absolute value of the difference between the number of vertices with different types is high, supports segregation and moreover, that large common neighborhoods are more decisive. As an application, we study the expected behavior of the FSP on two common random graph models with and without geometry: (1) For random geometric graphs, we show that the existence of an edge u,v makes a highly decisive common neighborhood for u and v more likely. Based on this, we prove the existence of a constant c > 0 such that the expected fraction of monochrome edges after the FSP is at least 1/2 + c. (2) For Erdős–Rényi graphs we show that large common neighborhoods are unlikely and that the expected fraction of monochrome edges after the FSP is at most 1/2 + o (1). Our results indicate that the cluster structure of the underlying graph has a significant impact on the obtained segregation strength.
@inproceedings{blasius2021impact, abstract = {Schelling’s classical segregation model gives a coherent explanation for the wide-spread phenomenon of residential segregation. We consider an agent-based saturated open-city variant, the Flip-Schelling-Process (FSP), in which agents, placed on a graph, have one out of two types and, based on the predominant type in their neighborhood, decide whether to changes their types; similar to a new agent arriving as soon as another agent leaves the vertex. We investigate the probability that an edge {u,v}is monochrome, i.e., that both vertices u and v have the same type in the FSP, and we provide a general framework for analyzing the influence of the underlying graph topology on residential segregation. In particular, for two adjacent vertices, we show that a highly decisive common neighborhood, i.e., a common neighborhood where the absolute value of the difference between the number of vertices with different types is high, supports segregation and moreover, that large common neighborhoods are more decisive. As an application, we study the expected behavior of the FSP on two common random graph models with and without geometry: (1) For random geometric graphs, we show that the existence of an edge {u,v} makes a highly decisive common neighborhood for u and v more likely. Based on this, we prove the existence of a constant c > 0 such that the expected fraction of monochrome edges after the FSP is at least 1/2 + c. (2) For Erdős–Rényi graphs we show that large common neighborhoods are unlikely and that the expected fraction of monochrome edges after the FSP is at most 1/2 + o (1). Our results indicate that the cluster structure of the underlying graph has a significant impact on the obtained segregation strength.}, author = {Bläsius, Thomas and Friedrich, Tobias and Krejca, Martin S. and Molitor, Louise}, booktitle = {International Symposium on Algorithms and Computation, (ISAAC) 2021}, keywords = {sys:relevantfor:ae thomasblaesius isaac louisemolitor martinskrejca tobiasfriedrich year2021}, pages = {29:1&ndash;29:17}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {The Impact of Geometry on Monochrome Regions in the Flip Schelling Process}, volume = 212, year = 2021 }

Antoniadis, Antonios; Kumar, Gunjan; Kumar, Nikhil Skeletons and Minimum Energy SchedulingInternational Symposium on Algorithms and Computation (ISAAC) 2021: 51:1–51:16
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Consider the problem where \(n\) jobs, each with a release time, a deadline and a required processing time are to be feasibly scheduled in a single- or multi-processor setting so as to minimize the total energy consumption of the schedule. A processor has two available states: a sleep state where no energy is consumed but also no processing can take place, and an active state which consumes energy at a rate of one, and in which jobs can be processed. Transitioning from the active to the sleep does not incur any further energy cost, but transitioning from the sleep to the active state requires \(q\) energy units. Jobs may be preempted and (in the multi-processor case) migrated. The single-processor case of the problem is known to be solvable in polynomial time via an involved dynamic program, whereas the only known approximation algorithm for the multi-processor case attains an approximation factor of 3 and is based on rounding the solution to a linear programming relaxation of the problem. In this work, we present efficient and combinatorial approximation algorithms for both the single- and the multi-processor setting. Before, only an algorithm based on linear programming was known for the multi-processor case. Our algorithms build upon the concept of a skeleton, a basic (and not necessarily feasible) schedule that captures the fact that some processor(s) must be active at some time point during an interval. Finally, we further demonstrate the power of skeletons by providing an 2-approximation algorithm for the multiprocessor case, thus improving upon the recent breakthrough 3-approximation result. Our algorithm is based on a novel rounding scheme of a linear-programming relaxation of the problem which incorporates skeletons.
@inproceedings{antoniadis2021skeletons, abstract = {Consider the problem where \(n\) jobs, each with a release time, a deadline and a required processing time are to be feasibly scheduled in a single- or multi-processor setting so as to minimize the total energy consumption of the schedule. A processor has two available states: a sleep state where no energy is consumed but also no processing can take place, and an active state which consumes energy at a rate of one, and in which jobs can be processed. Transitioning from the active to the sleep does not incur any further energy cost, but transitioning from the sleep to the active state requires \(q\) energy units. Jobs may be preempted and (in the multi-processor case) migrated. The single-processor case of the problem is known to be solvable in polynomial time via an involved dynamic program, whereas the only known approximation algorithm for the multi-processor case attains an approximation factor of 3 and is based on rounding the solution to a linear programming relaxation of the problem. In this work, we present efficient and combinatorial approximation algorithms for both the single- and the multi-processor setting. Before, only an algorithm based on linear programming was known for the multi-processor case. Our algorithms build upon the concept of a skeleton, a basic (and not necessarily feasible) schedule that captures the fact that some processor(s) must be active at some time point during an interval. Finally, we further demonstrate the power of skeletons by providing an 2-approximation algorithm for the multiprocessor case, thus improving upon the recent breakthrough 3-approximation result. Our algorithm is based on a novel rounding scheme of a linear-programming relaxation of the problem which incorporates skeletons.}, author = {Antoniadis, Antonios and Kumar, Gunjan and Kumar, Nikhil}, booktitle = {International Symposium on Algorithms and Computation (ISAAC)}, keywords = {isaac nikhilkumar year2021}, pages = {51:1-51:16}, title = {Skeletons and Minimum Energy Scheduling}, year = 2021 }

Casel, Katrin; Friedrich, Tobias; Issac, Davis; Klodt, Nicolas; Seifert, Lars; Zahn, Arthur A Color-blind 3-Approximation for Chromatic Correlation Clustering and Improved HeuristicsKnowledge Discovery and Data Mining (KDD) 2021: 882–891
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Chromatic Correlation Clustering (CCC) models clustering of objects with categorical pairwise relationships. The model can be viewed as clustering the vertices of a graph with edge-labels (colors). Bonchi et al. [KDD 2012] introduced it as a natural generalization of the well studied problem Correlation Clustering (CC), motivated by real-world applications from data-mining, social networks and bioinformatics. We give theoretical as well as practical contributions to the study of CCC. Our main theoretical contribution is an alternative analysis of the famous Pivot algorithm for CC. We show that, when simply run color-blind, Pivot is also a linear time 3-approximation for CCC. The previous best theoretical results for CCC were a 4-approximation with a high-degree polynomial runtime and a linear time 11-approximation, both by Anava et al. [WWW 2015]. While this theoretical result justifies Pivot as a baseline comparison for other heuristics, its blunt color-blindness performs poorly in practice. We develop a color-sensitive, practical heuristic we call Greedy Expansion that empirically outperforms all heuristics proposed for CCC so far, both on real-world and synthetic instances. Further, we propose a novel generalization of CCC allowing for multi-labelled edges. We argue that it is more suitable for many of the real-world applications and extend our results to this model.
@inproceedings{casel2021colorblind, abstract = {Chromatic Correlation Clustering (CCC) models clustering of objects with categorical pairwise relationships. The model can be viewed as clustering the vertices of a graph with edge-labels (colors). Bonchi et al. [KDD 2012] introduced it as a natural generalization of the well studied problem Correlation Clustering (CC), motivated by real-world applications from data-mining, social networks and bioinformatics. We give theoretical as well as practical contributions to the study of CCC. Our main theoretical contribution is an alternative analysis of the famous Pivot algorithm for CC. We show that, when simply run color-blind, Pivot is also a linear time 3-approximation for CCC. The previous best theoretical results for CCC were a 4-approximation with a high-degree polynomial runtime and a linear time 11-approximation, both by Anava et al. [WWW 2015]. While this theoretical result justifies Pivot as a baseline comparison for other heuristics, its blunt color-blindness performs poorly in practice. We develop a color-sensitive, practical heuristic we call Greedy Expansion that empirically outperforms all heuristics proposed for CCC so far, both on real-world and synthetic instances. Further, we propose a novel generalization of CCC allowing for multi-labelled edges. We argue that it is more suitable for many of the real-world applications and extend our results to this model.}, author = {Casel, Katrin and Friedrich, Tobias and Issac, Davis and Klodt, Nicolas and Seifert, Lars and Zahn, Arthur}, booktitle = {Knowledge Discovery and Data Mining (KDD)}, keywords = {sys:relevantfor:ae nicolasklodt katrincasel davisissac tobiasfriedrich arthurzahn kdd larsseifert year2021}, pages = {882&ndash;891}, publisher = {ACM}, title = {A Color-blind 3-Approximation for Chromatic Correlation Clustering and Improved Heuristics}, year = 2021 }

Bilò, Davide; Cohen, Sarel; Friedrich, Tobias; Schirneck, Martin Space-Efficient Fault-Tolerant Diameter OraclesMathematical Foundations of Computer Science (MFCS) 2021: 18:1–18:16
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
We design \(f\)-edge fault-tolerant diameter oracles (\(f\)-FDO, or simply FDO if \(f=1\)). For a given directed or undirected and possibly edge-weighted graph \(G\) with \(n\) vertices and \(m\) edges and a positive integer \(f\), we preprocess the graph and construct a data structure that, when queried with a set \(F\) of edges, where \(|F| \leq f\), returns the diameter of \(G - F\). An \(f\)-FDO has stretch \(\sigma \geq 1\) if the returned value \(\widehat D\) satisfies \(\operatornamediam(G - F) leq widehat D leq sigma \operatornamediam(G - F)\). For the case of a single edge failure (\(f=1\)) in an unweighted directed graph, there exists an approximate FDO by Henzinger et al. [ITCS 2017] with stretch \((1+\varepsilon)\), constant query time, space \(O(m)\), and a combinatorial preprocessing time of \(\widetildeO(mn + n^1.5 \sqrt{Dm/\varepsilon})\), where \(D\) is the diameter. We present a near-optimal FDO with the same stretch, query time, and space. It has a preprocessing time of \(\widetildeO(mn + n^2/\varepsilon)\), which is better for any constant \(\varepsilon > 0\). The preprocessing time nearly matches a conditional lower bound for combinatorial algorithms, also by Henzinger et al. When using fast matrix multiplication instead, we achieve a preprocessing time of \(\widetildeO(n^2.5794 + n^2/\varepsilon)\). We further prove an information-theoretic lower bound showing that any FDO with stretch better than \(3/2\) requires \(\Omega(m)\) bits of space. Thus, for constant \(0 < \varepsilon < 3/2\), our combinatorial \((1+ \varepsilon)\)-approximate FDO is near-optimal in all the parameters. In the case of multiple edge failures (\(f>1\)) in undirected graphs with non-negative edge weights, we give an \(f\)-FDO with stretch \((f+2)\), query time \(O(f^2\log^2{n})\), \(\widetildeO(fn)\) space, and preprocessing time \(\widetildeO(fm)\). We complement this with a lower bound excluding any finite stretch in \(o(fn)\) space. Many real-world networks have polylogarithmic diameter. We show that for those graphs and up to \(f = o(\log n/ \log\log n)\) failures one can swap approximation for query time and space. We present an exact combinatorial \(f\)-FDO with preprocessing time \(mn^{1+o(1)}\), query time \(n^{o(1)}\), and space \(n^{2+o(1)}\). With fast matrix multiplication, the preprocessing time can be improved to \(n^{\omega+o(1)}\), where \(\omega < 2.373\) is the matrix multiplication exponent.
@inproceedings{bilo2021spaceefficient, abstract = {We design \(f\)-edge fault-tolerant diameter oracles (\(f\)-FDO, or simply FDO if \(f=1\)). For a given directed or undirected and possibly edge-weighted graph \(G\) with \(n\) vertices and \(m\) edges and a positive integer \(f\), we preprocess the graph and construct a data structure that, when queried with a set \(F\) of edges, where \(|F| \leq f\), returns the diameter of \(G - F\). An \(f\)-FDO has stretch \(\sigma \geq 1\) if the returned value \(\widehat D\) satisfies \(\operatorname{diam}(G - F) \leq \widehat D \leq \sigma \operatorname{diam}(G - F)\). For the case of a single edge failure (\(f=1\)) in an unweighted directed graph, there exists an approximate FDO by Henzinger et al. [ITCS 2017] with stretch \((1+\varepsilon)\), constant query time, space \(O(m)\), and a combinatorial preprocessing time of \(\widetilde{O}(mn + n^{1.5} \sqrt{Dm/\varepsilon})\), where \(D\) is the diameter. We present a near-optimal FDO with the same stretch, query time, and space. It has a preprocessing time of \(\widetilde{O}(mn + n^2/\varepsilon)\), which is better for any constant \(\varepsilon > 0\). The preprocessing time nearly matches a conditional lower bound for combinatorial algorithms, also by Henzinger et al. When using fast matrix multiplication instead, we achieve a preprocessing time of \(\widetilde{O}(n^{2.5794} + n^2/\varepsilon)\). We further prove an information-theoretic lower bound showing that any FDO with stretch better than \(3/2\) requires \(\Omega(m)\) bits of space. Thus, for constant \(0 < \varepsilon < 3/2\), our combinatorial \((1+ \varepsilon)\)-approximate FDO is near-optimal in all the parameters. In the case of multiple edge failures (\(f>1\)) in undirected graphs with non-negative edge weights, we give an \(f\)-FDO with stretch \((f+2)\), query time \(O(f^2\log^2{n})\), \(\widetilde{O}(fn)\) space, and preprocessing time \(\widetilde{O}(fm)\). We complement this with a lower bound excluding any finite stretch in \(o(fn)\) space. Many real-world networks have polylogarithmic diameter. We show that for those graphs and up to \(f = o(\log n/ \log\log n)\) failures one can swap approximation for query time and space. We present an exact combinatorial \(f\)-FDO with preprocessing time \(mn^{1+o(1)}\), query time \(n^{o(1)}\), and space \(n^{2+o(1)}\). With fast matrix multiplication, the preprocessing time can be improved to \(n^{\omega+o(1)}\), where \(\omega < 2.373\) is the matrix multiplication exponent.}, author = {Bilò, Davide and Cohen, Sarel and Friedrich, Tobias and Schirneck, Martin}, booktitle = {Mathematical Foundations of Computer Science (MFCS)}, keywords = {sarelcohen davidebilo tobiasfriedrich mfcs year2021 martinschirneck}, pages = {18:1&ndash;18:16}, title = {Space-Efficient Fault-Tolerant Diameter Oracles}, year = 2021 }

Kißig, Otto; Taraz, Martin; Cohen, Sarel; Doskoč, Vanja; Friedrich, Tobias Drug Repurposing for Multiple COVID Strains using Collaborative FilteringICLR Workshop on Machine Learning for Preventing and Combating Pandemics (MLPCP@ICLR) 2021
[ Abstract ] [ BibTeX ] [ Download ]
 
The ongoing COVID-19 pandemic demands for a swift discovery of suitable treatments. The development of completely new compounds for such a novel disease is a challenging, time intensive process. This amplifies the relevance of drug repurposing, a technique where existing drugs are used to treat other diseases. A common bioinformatical approach to this is based on knowledge graphs, which compile relationships between drugs, diseases, genes and other biomedical entities. Then, graph neural networks (GNNs) are used for the drug repurposing task as they provide a good link prediction performance on such knowledge graphs. Building on state-of-the-art GNN research, Doshi & Chepuri (2020) construct the remarkable model DR-COVID. We re-implement their model and extend the approach to perform significantly better. We propose and evaluate several strategies for the aggregation of link predictions into drug recommendation rankings. With the help of clustering of similar target diseases we improve the model by a substantial margin, compiling a top-100 ranking of candidates including 32 currently being in COVID-19-related clinical trials. Regarding the re-implementation, we offer more flexibility in the selection of the graph neighborhood sizes fed into the model and reduce the training time significantly by making use of data parallelism.
@inproceedings{kissig2021repurposingcollaborativefiltering, abstract = {The ongoing COVID-19 pandemic demands for a swift discovery of suitable treatments. The development of completely new compounds for such a novel disease is a challenging, time intensive process. This amplifies the relevance of drug repurposing, a technique where existing drugs are used to treat other diseases. A common bioinformatical approach to this is based on knowledge graphs, which compile relationships between drugs, diseases, genes and other biomedical entities. Then, graph neural networks (GNNs) are used for the drug repurposing task as they provide a good link prediction performance on such knowledge graphs. Building on state-of-the-art GNN research, Doshi \& Chepuri (2020) construct the remarkable model DR-COVID. We re-implement their model and extend the approach to perform significantly better. We propose and evaluate several strategies for the aggregation of link predictions into drug recommendation rankings. With the help of clustering of similar target diseases we improve the model by a substantial margin, compiling a top-100 ranking of candidates including 32 currently being in COVID-19-related clinical trials. Regarding the re-implementation, we offer more flexibility in the selection of the graph neighborhood sizes fed into the model and reduce the training time significantly by making use of data parallelism.}, author = {Kißig, Otto and Taraz, Martin and Cohen, Sarel and Doskoč, Vanja and Friedrich, Tobias}, booktitle = {ICLR Workshop on Machine Learning for Preventing and Combating Pandemics (MLPCP@ICLR)}, keywords = {sarelcohen ottokissig vanjadoskoc mlpcp@iclr tobiasfriedrich martintaraz year2021}, title = {Drug Repurposing for Multiple COVID Strains using Collaborative Filtering}, year = 2021 }

Atzberger, Daniel; Cech, Tim; de la Haye, Merlin; Söchting, Maximilian; Scheibel, Willy; Limberger, Daniel; Döllner, Jürgen Software Forest: A Visualization of Semantic Similarities in Source Code using a Tree MetaphorProceedings of the 16th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications -- Volume 3 IVAPP 2021: 112–122
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Software visualization techniques provide effective means for program comprehension tasks as they allow developers to interactively explore large code bases. A frequently encountered task during software development is the detection of source code files of similar semantic. To assist this task we present Software Forest, a novel 2.5D software visualization that enables interactive exploration of semantic similarities within a software system, illustrated as a forest. The underlying layout results from the analysis of the vocabulary of the software documents using Latent Dirichlet Allocation and Multidimensional Scaling and therefore reflects the semantic similarity between source code files. By mapping properties of a software entity, e.g., size metrics or trend data, to visual variables encoded by various, figurative tree meshes, aspects of a software system can be displayed. This concept is complemented with implementation details as well as a discussion on applications.
@inproceedings{atzberger2021-softwareforest-ae-version, abstract = {Software visualization techniques provide effective means for program comprehension tasks as they allow developers to interactively explore large code bases. A frequently encountered task during software development is the detection of source code files of similar semantic. To assist this task we present Software Forest, a novel 2.5D software visualization that enables interactive exploration of semantic similarities within a software system, illustrated as a forest. The underlying layout results from the analysis of the vocabulary of the software documents using Latent Dirichlet Allocation and Multidimensional Scaling and therefore reflects the semantic similarity between source code files. By mapping properties of a software entity, e.g., size metrics or trend data, to visual variables encoded by various, figurative tree meshes, aspects of a software system can be displayed. This concept is complemented with implementation details as well as a discussion on applications.}, author = {Atzberger, Daniel and Cech, Tim and de la Haye, Merlin and Söchting, Maximilian and Scheibel, Willy and Limberger, Daniel and Döllner, Jürgen}, booktitle = {Proceedings of the 16th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications &ndash; Volume 3 IVAPP}, keywords = {danielatzberger timcech juergendoellner maximiliansoechting daniellimberger ivapp merlindelahaye willyscheibel year2021}, organization = {INSTICC}, pages = {112&ndash;122}, publisher = {SciTePress}, title = {Software Forest: A Visualization of Semantic Similarities in Source Code using a Tree Metaphor}, year = 2021 }

Friedrich, Tobias; Neumann, Frank; Rothenberger, Ralf; Sutton, Andrew M. Solving Non-Uniform Planted and Filtered Random SAT Formulas GreedilyTheory and Applications of Satisfiability Testing (SAT) 2021: 188–206
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Recently, there has been an interest in studying non-uniform random \(k\)-satisfiability (\(k\)-SAT) models in order to address the non-uniformity of formulas arising from real-world applications. While uniform random \(k\)-SAT has been extensively studied from both a theoretical and experimental perspective, understanding the algorithmic complexity of heterogeneous distributions is still an open challenge. When a sufficiently dense formula is guaranteed to be satisfiable by conditioning or a planted assignment, it is well-known that uniform random \(k\)-SAT is easy on average. We generalize this result to the broad class of non-uniform random \(k\)-SAT models that are characterized only by an ensemble of distributions over variables with a mild balancing condition. This balancing condition rules out extremely skewed distributions in which nearly half the variables occur less frequently than a small constant fraction of the most frequent variables, but generalizes recently studied non-uniform \(k\)-SAT distributions such as power-law and geometric formulas. We show that for all formulas generated from this model of at least logarithmic densities, a simple greedy algorithm can find a solution with high probability. As a side result we show that the total variation distance between planted and filtered (conditioned on satisfiability) models is \(o(1)\) once the planted model produces formulas with a unique solution with probability \(1-o(1)\). This holds for all random \(k\)-SAT models where the signs of variables are drawn uniformly and independently at random.
@inproceedings{rothenberger2021solving, abstract = {Recently, there has been an interest in studying non-uniform random \(k\)-satisfiability (\(k\)-SAT) models in order to address the non-uniformity of formulas arising from real-world applications. While uniform random \(k\)-SAT has been extensively studied from both a theoretical and experimental perspective, understanding the algorithmic complexity of heterogeneous distributions is still an open challenge. When a sufficiently dense formula is guaranteed to be satisfiable by conditioning or a planted assignment, it is well-known that uniform random \(k\)-SAT is easy on average. We generalize this result to the broad class of non-uniform random \(k\)-SAT models that are characterized only by an ensemble of distributions over variables with a mild balancing condition. This balancing condition rules out extremely skewed distributions in which nearly half the variables occur less frequently than a small constant fraction of the most frequent variables, but generalizes recently studied non-uniform \(k\)-SAT distributions such as power-law and geometric formulas. We show that for all formulas generated from this model of at least logarithmic densities, a simple greedy algorithm can find a solution with high probability. As a side result we show that the total variation distance between planted and filtered (conditioned on satisfiability) models is \(o(1)\) once the planted model produces formulas with a unique solution with probability \(1-o(1)\). This holds for all random \(k\)-SAT models where the signs of variables are drawn uniformly and independently at random.}, author = {Friedrich, Tobias and Neumann, Frank and Rothenberger, Ralf and Sutton, Andrew M.}, booktitle = {Theory and Applications of Satisfiability Testing (SAT)}, keywords = {sat tobiasfriedrich frankneumann andrewmsutton ralfrothenberger year2021}, pages = {188-206}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {Solving Non-Uniform Planted and Filtered Random SAT Formulas Greedily}, volume = 12831, year = 2021 }

Bläsius, Thomas; Friedrich, Tobias; Katzmann, Maximilian Force-Directed Embedding of Scale-Free Networks in the Hyperbolic PlaneSymposium on Experimental Algorithms (SEA) 2021: 22:1–22:18
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Force-directed drawing algorithms are the most commonly used approach to visualize networks. While they are usually very robust, the performance of Euclidean spring embedders decreases if the graph exhibits the high level of heterogeneity that typically occurs in scale-free real-world networks. As heterogeneity naturally emerges from hyperbolic geometry (in fact, scale-free networks are often perceived to have an underlying hyperbolic geometry), it is natural to embed them into the hyperbolic plane instead. Previous techniques that produce hyperbolic embeddings usually make assumptions about the given network, which (if not met) impairs the quality of the embedding. It is still an open problem to adapt force-directed embedding algorithms to make use of the heterogeneity of the hyperbolic plane, while also preserving their robustness. We identify fundamental differences between the behavior of spring embedders in Euclidean and hyperbolic space, and adapt the technique to take advantage of the heterogeneity of the hyperbolic plane.
@inproceedings{bfk-fdesfnhp-2021, abstract = {Force-directed drawing algorithms are the most commonly used approach to visualize networks. While they are usually very robust, the performance of Euclidean spring embedders decreases if the graph exhibits the high level of heterogeneity that typically occurs in scale-free real-world networks. As heterogeneity naturally emerges from hyperbolic geometry (in fact, scale-free networks are often perceived to have an underlying hyperbolic geometry), it is natural to embed them into the hyperbolic plane instead. Previous techniques that produce hyperbolic embeddings usually make assumptions about the given network, which (if not met) impairs the quality of the embedding. It is still an open problem to adapt force-directed embedding algorithms to make use of the heterogeneity of the hyperbolic plane, while also preserving their robustness. We identify fundamental differences between the behavior of spring embedders in Euclidean and hyperbolic space, and adapt the technique to take advantage of the heterogeneity of the hyperbolic plane.}, author = {Bläsius, Thomas and Friedrich, Tobias and Katzmann, Maximilian}, booktitle = {Symposium on Experimental Algorithms (SEA)}, keywords = {thomasblaesius tobiasfriedrich maximiliankatzmann year2021 sea}, pages = {22:1-22:18}, title = {Force-Directed Embedding of Scale-Free Networks in the Hyperbolic Plane}, year = 2021 }

Bläsius, Thomas; Friedrich, Tobias; Göbel, Andreas; Levy, Jordi; Rothenberger, Ralf The Impact of Heterogeneity and Geometry on the Proof Complexity of Random SatisfiabilitySymposium on Discrete Algorithms (SODA) 2021: 42–53
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Satisfiability is considered the canonical NP-complete problem and is used as a starting point for hardness reductions in theory, while in practice heuristic SAT solving algorithms can solve large-scale industrial SAT instances very efficiently. This disparity between theory and practice is believed to be a result of inherent properties of industrial SAT instances that make them tractable. Two characteristic properties seem to be prevalent in the majority of real-world SAT instances, heterogeneous degree distribution and locality. To understand the impact of these two properties on SAT, we study the proof complexity of random k-SAT models that allow to control heterogeneity and locality. Our findings show that heterogeneity alone does not make SAT easy as heterogeneous random k-SAT instances have superpolynomial resolution size. This implies intractability of these instances for modern SAT-solvers. On the other hand, modeling locality with an underlying geometry leads to small unsatisfiable subformulas, which can be found within polynomial time. A key ingredient for the result on geometric random k-SAT can be found in the complexity of higher-order Voronoi diagrams. As an additional technical contribution, we show an upper bound on the number of non-empty Voronoi regions, that holds for points with random positions in a very general setting. In particular, it covers arbitrary p-norms, higher dimensions, and weights affecting the area of influence of each point multiplicatively. Our bound is linear in the total weight. This is in stark contrast to quadratic lower bounds for the worst case.
@inproceedings{blasius2021impact, abstract = {Satisfiability is considered the canonical NP-complete problem and is used as a starting point for hardness reductions in theory, while in practice heuristic SAT solving algorithms can solve large-scale industrial SAT instances very efficiently. This disparity between theory and practice is believed to be a result of inherent properties of industrial SAT instances that make them tractable. Two characteristic properties seem to be prevalent in the majority of real-world SAT instances, heterogeneous degree distribution and locality. To understand the impact of these two properties on SAT, we study the proof complexity of random k-SAT models that allow to control heterogeneity and locality. Our findings show that heterogeneity alone does not make SAT easy as heterogeneous random k-SAT instances have superpolynomial resolution size. This implies intractability of these instances for modern SAT-solvers. On the other hand, modeling locality with an underlying geometry leads to small unsatisfiable subformulas, which can be found within polynomial time. A key ingredient for the result on geometric random k-SAT can be found in the complexity of higher-order Voronoi diagrams. As an additional technical contribution, we show an upper bound on the number of non-empty Voronoi regions, that holds for points with random positions in a very general setting. In particular, it covers arbitrary p-norms, higher dimensions, and weights affecting the area of influence of each point multiplicatively. Our bound is linear in the total weight. This is in stark contrast to quadratic lower bounds for the worst case.}, author = {Bläsius, Thomas and Friedrich, Tobias and Göbel, Andreas and Levy, Jordi and Rothenberger, Ralf}, booktitle = {Symposium on Discrete Algorithms (SODA)}, keywords = {jordilevy thomasblaesius andreasgoebel tobiasfriedrich ralfrothenberger soda year2021}, pages = {42-53}, publisher = {SIAM}, title = {The Impact of Heterogeneity and Geometry on the Proof Complexity of Random Satisfiability}, year = 2021 }

Friedemann, Wilhelm; Friedrich, Tobias; Gawendowicz, Hans; Lenzner, Pascal; Melnichenko, Anna; Peters, Jannik; Stephan, Daniel; Vaichenker, Michael Efficiency and Stability in Euclidean Network DesignSymposium on Parallelism in Algorithms and Architectures (SPAA) 2021: 232–242
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Network Design problems typically ask for a minimum cost sub-network from a given host network. This classical point-of-view assumes a central authority enforcing the optimum solution. But how should networks be designed to cope with selfish agents that own parts of the network? In this setting, minimum cost networks may be very unstable in that agents will deviate from a proposed solution if this decreases their individual cost. Hence, designed networks should be both efficient in terms of total cost and stable in terms of the agents' willingness to accept the network. We study this novel type of Network Design problem by investigating the creation of \($(\beta,\gamma)$\)-networks, that are in \($\beta$\)-approximate Nash equilibrium and have a total cost of at most \($\gamma$\) times the optimal cost, for the recently proposed Euclidean Generalized Network Creation Game by Bilò et al.SPAA2019. There, \($n$\) agents corresponding to points in Euclidean space create costly edges among themselves to optimize their centrality in the created network. Our main result is a simple \($\mathcal{O(n^2)$\)-time algorithm that computes a \($(\beta,\beta)$\)-network with low \($\beta$\) for any given set of points. Moreover, on integer grid point sets or random point sets our algorithm achieves a low constant \($\beta$\). Besides these results for the Euclidean model, we discuss a generalization of our algorithm to instances with arbitrary, even non-metric, edge lengths. Moreover, in contrast to these algorithmic results, we show that no such positive results are possible when focusing on either optimal networks, i.e., \($(\beta,1)$\)-networks, or perfectly stable networks, i.e., \($(1,\gamma)$\)-networks, as in both cases NP-hard problems arise, there exist instances with very unstable optimal networks, and there are instances for perfectly stable networks with high total cost. Along the way, we significantly improve several results from Bilò et al. and we asymptotically resolve their conjecture about the Price of Anarchy by providing a tight bound.
@inproceedings{friedemann2021efficiency, abstract = {Network Design problems typically ask for a minimum cost sub-network from a given host network. This classical point-of-view assumes a central authority enforcing the optimum solution. But how should networks be designed to cope with selfish agents that own parts of the network? In this setting, minimum cost networks may be very unstable in that agents will deviate from a proposed solution if this decreases their individual cost. Hence, designed networks should be both efficient in terms of total cost and stable in terms of the agents' willingness to accept the network. We study this novel type of Network Design problem by investigating the creation of $(\beta,\gamma)$-networks, that are in $\beta$-approximate Nash equilibrium and have a total cost of at most $\gamma$ times the optimal cost, for the recently proposed Euclidean Generalized Network Creation Game by Bilò et al.SPAA2019. There, $n$ agents corresponding to points in Euclidean space create costly edges among themselves to optimize their centrality in the created network. Our main result is a simple $\mathcal{O}(n^2)$-time algorithm that computes a $(\beta,\beta)$-network with low $\beta$ for any given set of points. Moreover, on integer grid point sets or random point sets our algorithm achieves a low constant $\beta$. Besides these results for the Euclidean model, we discuss a generalization of our algorithm to instances with arbitrary, even non-metric, edge lengths. Moreover, in contrast to these algorithmic results, we show that no such positive results are possible when focusing on either optimal networks, i.e., $(\beta,1)$-networks, or perfectly stable networks, i.e., $(1,\gamma)$-networks, as in both cases NP-hard problems arise, there exist instances with very unstable optimal networks, and there are instances for perfectly stable networks with high total cost. Along the way, we significantly improve several results from Bilò et al. and we asymptotically resolve their conjecture about the Price of Anarchy by providing a tight bound.}, author = {Friedemann, Wilhelm and Friedrich, Tobias and Gawendowicz, Hans and Lenzner, Pascal and Melnichenko, Anna and Peters, Jannik and Stephan, Daniel and Vaichenker, Michael}, booktitle = {Symposium on Parallelism in Algorithms and Architectures (SPAA)}, keywords = {hansgawendowicz sys:relevantfor:ae spaa tobiasfriedrich annamelnichenko pascallenzner year2021}, pages = {232&ndash;242}, publisher = {ASM}, title = {Efficiency and Stability in Euclidean Network Design}, year = 2021 }

Kißig, Otto; Taraz, Martin; Cohen, Sarel; Friedrich, Tobias Drug Repurposing Using Link Prediction on Knowledge GraphsICML Workshop on Computational Biology (WCB@ICML) 2021: 742–753
[ Abstract ] [ BibTeX ] [ DOI ] [ Download ]
 
The active global SARS-CoV-2 pandemic caused more than 167 million cases and 3.4 million deaths worldwide. The development of completely new drugs for such a novel disease is a challenging, time intensive process and despite researchers around the world working on this task, no effective treatments have been developed yet. This emphasizes the importance of drug repurposing, where treatments are found among existing drugs that are meant for different diseases. A common approach to this is based on knowledge graphs, that condense relationships between entities like drugs, diseases and genes. Graph neural networks (GNNs) can then be used for the task at hand by predicting links in such knowledge graphs. Expanding on state-of-the-art GNN research, Doshi et al. recently developed the Dr-COVID model. We further extend their work using additional output interpretation strategies. The best aggregation strategy derives a top-100 ranking of candidate drugs, 32 of which currently being in COVID-19-related clinical trials. Moreover, we present an alternative application for the model, the generation of additional candidates based on a given pre-selection of drug candidates using collaborative filtering. In addition, we improved the implementation of the Dr-COVID model by significantly shortening the inference and pre-processing time by exploiting data-parallelism. As drug repurposing is a task that requires high computation and memory resources, we further accelerate the post-processing phase using a new emerging hardware—we propose a new approach to leverage the use of high-capacity Non-Volatile Memory for aggregate drug ranking.
@inproceedings{kissig2021repurposingknowledgegraph, abstract = {The active global SARS-CoV-2 pandemic caused more than 167 million cases and 3.4 million deaths worldwide. The development of completely new drugs for such a novel disease is a challenging, time intensive process and despite researchers around the world working on this task, no effective treatments have been developed yet. This emphasizes the importance of drug repurposing, where treatments are found among existing drugs that are meant for different diseases. A common approach to this is based on knowledge graphs, that condense relationships between entities like drugs, diseases and genes. Graph neural networks (GNNs) can then be used for the task at hand by predicting links in such knowledge graphs. Expanding on state-of-the-art GNN research, Doshi et al. recently developed the Dr-COVID model. We further extend their work using additional output interpretation strategies. The best aggregation strategy derives a top-100 ranking of candidate drugs, 32 of which currently being in COVID-19-related clinical trials. Moreover, we present an alternative application for the model, the generation of additional candidates based on a given pre-selection of drug candidates using collaborative filtering. In addition, we improved the implementation of the Dr-COVID model by significantly shortening the inference and pre-processing time by exploiting data-parallelism. As drug repurposing is a task that requires high computation and memory resources, we further accelerate the post-processing phase using a new emerging hardware—we propose a new approach to leverage the use of high-capacity Non-Volatile Memory for aggregate drug ranking.}, author = {Kißig, Otto and Taraz, Martin and Cohen, Sarel and Friedrich, Tobias}, booktitle = {ICML Workshop on Computational Biology (WCB@ICML)}, keywords = {sarelcohen ottokissig sys:relevantfor:ae tobiasfriedrich martintaraz year2021 wcp@icml}, pages = {742&ndash;753}, title = {Drug Repurposing Using Link Prediction on Knowledge Graphs}, year = 2021 }

2020

Cseh, Ágnes; Fleiner, Tamás The Complexity of Cake Cutting with Unequal SharesACM Transactions on Algorithms 2020: 1–21
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
An unceasing problem of our prevailing society is the fair division of goods. The problem of proportional cake cutting focuses on dividing a heterogeneous and divisible resource, the cake, among n players who value pieces according to their own measure function. The goal is to assign each player a not necessarily connected part of the cake that the player evaluates at least as much as her proportional share. In this article, we investigate the problem of proportional division with unequal shares, where each player is entitled to receive a predetermined portion of the cake. Our main contribution is threefold. First we present a protocol for integer demands, which delivers a proportional solution in fewer queries than all known proto- cols. By giving a matching lower bound, we then show that our protocol is asymptotically the fastest possible. Finally, we turn to irrational demands and solve the proportional cake cutting problem by reducing it to the same problem with integer demands only. All results remain valid in a highly general cake cutting model, which can be of independent interest.
@article{CF20, abstract = {An unceasing problem of our prevailing society is the fair division of goods. The problem of proportional cake cutting focuses on dividing a heterogeneous and divisible resource, the cake, among n players who value pieces according to their own measure function. The goal is to assign each player a not necessarily connected part of the cake that the player evaluates at least as much as her proportional share. In this article, we investigate the problem of proportional division with unequal shares, where each player is entitled to receive a predetermined portion of the cake. Our main contribution is threefold. First we present a protocol for integer demands, which delivers a proportional solution in fewer queries than all known proto- cols. By giving a matching lower bound, we then show that our protocol is asymptotically the fastest possible. Finally, we turn to irrational demands and solve the proportional cake cutting problem by reducing it to the same problem with integer demands only. All results remain valid in a highly general cake cutting model, which can be of independent interest.}, address = {New York, NY, USA}, author = {Cseh, Ágnes and Fleiner, Tamás}, journal = {ACM Transactions on Algorithms}, keywords = {talg sys:relevantfor:ae tamasfleiner agnescseh year2020}, month = {jun}, number = 3, pages = {1-21}, publisher = {Association for Computing Machinery}, title = {The Complexity of Cake Cutting with Unequal Shares}, volume = 16, year = 2020 }

Shi, Feng; Schirneck, Martin; Friedrich, Tobias; Kötzing, Timo; Neumann, Frank Correction to: Reoptimization Time Analysis of Evolutionary Algorithms on Linear Functions Under Dynamic Uniform ConstraintsAlgorithmica 2020: 3117–3123
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
In the article "Reoptimization Time Analysis of Evolutionary Algorithms on Linear Functions Under Dynamic Uniform Constraints", we claimed a worst-case runtime of \(O(nD \log D)\) and \(O(nD)\) for the Multi-Objective Evolutionary Algorithm and the Multi-Objective \((\mu+(\lambda, \lambda))\) Genetic Algorithm, respectively, on linear profit functions under dynamic uniform constraint, where \(D = |B − B^*|\) denotes the difference between the original constraint bound \(B\) and the new one \(B^*\) . The technique used to prove these results contained an error. We correct this mistake and show a weaker bound of \(O(nD^2)\) for both algorithms instead.
@article{shi20correction, abstract = {In the article "Reoptimization Time Analysis of Evolutionary Algorithms on Linear Functions Under Dynamic Uniform Constraints", we claimed a worst-case runtime of \(O(nD \log D)\) and \(O(nD)\) for the Multi-Objective Evolutionary Algorithm and the Multi-Objective \((\mu+(\lambda, \lambda))\) Genetic Algorithm, respectively, on linear profit functions under dynamic uniform constraint, where \(D = |B − B^*|\) denotes the difference between the original constraint bound \(B\) and the new one \(B^*\) . The technique used to prove these results contained an error. We correct this mistake and show a weaker bound of \(O(nD^2)\) for both algorithms instead.}, author = {Shi, Feng and Schirneck, Martin and Friedrich, Tobias and Kötzing, Timo and Neumann, Frank}, journal = {Algorithmica}, keywords = {algorithmica timokoetzing fengshi tobiasfriedrich frankneumann martinschirneck year2020}, number = 10, pages = {3117-3123}, title = {Correction to: Reoptimization Time Analysis of Evolutionary Algorithms on Linear Functions Under Dynamic Uniform Constraints}, volume = 82, year = 2020 }

Chauhan, Ankit; Friedrich, Tobias; Rothenberger, Ralf Greed is Good for Deterministic Scale-Free NetworksAlgorithmica 2020: 3338–3389
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Large real-world networks typically follow a power-law degree distribution. To study such networks, numerous random graph models have been proposed. However, real-world networks are not drawn at random. Therefore, Brach, Cygan, Lacki, and Sankowski [SODA 2016] introduced two natural deterministic conditions: (1) a power-law upper bound on the degree distribution (PLB-U) and (2) power-law neighborhoods, that is, the degree distribution of neighbors of each vertex is also upper bounded by a power law (PLB-N). They showed that many real-world networks satisfy both deterministic properties and exploit them to design faster algorithms for a number of classical graph problems. We complement the work of Brach et al. by showing that some well-studied random graph models exhibit both the mentioned PLB properties and additionally also a power-law lower bound on the degree distribution (PLB-L). All three properties hold with high probability for Chung-Lu Random Graphs and Geometric Inhomogeneous Random Graphs and almost surely for Hyperbolic Random Graphs. As a consequence, all results of Brach et al. also hold with high probability or almost surely for those random graph classes. In the second part of this work we study three classical NP-hard combinatorial optimization problems on PLB networks. It is known that on general graphs with maximum degree \(\Delta\), a greedy algorithm, which chooses nodes in the order of their degree, only achieves a \(\Omega(\ln \Delta)\)-approximation for Minimum Vertex Cover and Minimum Dominating Set, and a \(\Omega(\Delta)\)-approximation for Maximum Independent Set. We prove that the PLB-U property suffices for the greedy approach to achieve a constant-factor approximation for all three problems. We also show that all three combinatorial optimization problems are APX-complete even if all PLB-properties holds hence, PTAS cannot be expected unless P=NP.
@article{cfr-gigfdsn-2020, abstract = {Large real-world networks typically follow a power-law degree distribution. To study such networks, numerous random graph models have been proposed. However, real-world networks are not drawn at random. Therefore, Brach, Cygan, Lacki, and Sankowski [SODA 2016] introduced two natural deterministic conditions: (1) a power-law upper bound on the degree distribution (PLB-U) and (2) power-law neighborhoods, that is, the degree distribution of neighbors of each vertex is also upper bounded by a power law (PLB-N). They showed that many real-world networks satisfy both deterministic properties and exploit them to design faster algorithms for a number of classical graph problems. We complement the work of Brach et al. by showing that some well-studied random graph models exhibit both the mentioned PLB properties and additionally also a power-law lower bound on the degree distribution (PLB-L). All three properties hold with high probability for Chung-Lu Random Graphs and Geometric Inhomogeneous Random Graphs and almost surely for Hyperbolic Random Graphs. As a consequence, all results of Brach et al. also hold with high probability or almost surely for those random graph classes. In the second part of this work we study three classical NP-hard combinatorial optimization problems on PLB networks. It is known that on general graphs with maximum degree \(\Delta\), a greedy algorithm, which chooses nodes in the order of their degree, only achieves a \(\Omega(\ln \Delta)\)-approximation for Minimum Vertex Cover and Minimum Dominating Set, and a \(\Omega(\Delta)\)-approximation for Maximum Independent Set. We prove that the PLB-U property suffices for the greedy approach to achieve a constant-factor approximation for all three problems. We also show that all three combinatorial optimization problems are APX-complete even if all PLB-properties holds hence, PTAS cannot be expected unless P=NP.}, author = {Chauhan, Ankit and Friedrich, Tobias and Rothenberger, Ralf}, journal = {Algorithmica}, keywords = {algorithmica sys:relevantfor:ae tobiasfriedrich ralfrothenberger ankitchauhan year2020}, month = {jun}, pages = {3338–3389}, title = {Greed is Good for Deterministic Scale-Free Networks}, volume = 82, year = 2020 }

Ghorbani, Ebrahim; Haemers, Willem H.; Reza Maimani, Hamid; Parsaei Majd, Leila On sign-symmetric signed graphsArs Mathematica Contemporane 2020: 83–93
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
A signed graph is said to be sign-symmetric if it is switching isomorphic to its negation. Bipartite signed graphs are trivially sign-symmetric. We give new constructions of non-bipartite sign-symmetric signed graphs. Sign-symmetric signed graphs have a symmetric spectrum but not the other way around. We present constructions of signed graphs with symmetric spectra which are not sign-symmetric. This, in particular answers a problem posed by Belardo, Cioabua}, Koolen, and Wang (2018).
@article{ghorbani2020signsymmetric, abstract = {A signed graph is said to be sign-symmetric if it is switching isomorphic to its negation. Bipartite signed graphs are trivially sign-symmetric. We give new constructions of non-bipartite sign-symmetric signed graphs. Sign-symmetric signed graphs have a symmetric spectrum but not the other way around. We present constructions of signed graphs with symmetric spectra which are not sign-symmetric. This, in particular answers a problem posed by Belardo, Cioab\u{a}, Koolen, and Wang (2018).}, author = {Ghorbani, Ebrahim and Haemers, Willem H. and Reza Maimani, Hamid and Parsaei Majd, Leila}, journal = {Ars Mathematica Contemporane}, keywords = {leilaparsaeimajd sys:relevantfor:ae hamidrezamaimani ebrahimghorbani amc willemhhaemers year2020}, pages = {83&ndash;93}, title = {On sign-symmetric signed graphs}, year = 2020 }

Casel, Katrin; Dreier, Jan; Fernau, Henning; Gobbert, Moritz; Kuinke, Philipp; Sanchez Villaamil, Fernando; Schmid, Markus L.; van Leeuwen, Erik Jan Complexity of independency and cliquy treesDiscrete Applied Mathematics 2020: 2–15
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
An independency (cliquy) tree of an \(n\)-vertex graph \(G\) is a spanning tree of \(G\) in which the set of leaves induces an independent set (clique). We study the problems of minimizing or maximizing the number of leaves of such trees, and fully characterize their parameterized complexity. We show that all four variants of deciding if an independency/cliquy tree with at least/most \(\ell\) leaves exists parameterized by \(\ell\) are either para-NP- or W[1]-hard. We prove that minimizing the number of leaves of a cliquy tree parameterized by the number of internal vertices is para-NP-hard too. However, we show that minimizing the number of leaves of an independency tree parameterized by the number \(k\) of internal vertices has an \(O^*(4^k)\)-time algorithm and a \(2k\) vertex kernel. Moreover, we prove that maximizing the number of leaves of an independency/cliquy tree parameterized by the number \(k\) of internal vertices both have an \(O^*(18^k)\)-time algorithm and an \(O(k\, 2^k)\) vertex kernel, but no polynomial kernel unless the polynomial hierarchy collapses to the third level. Finally, we present an \(O(3^n f(n))\)-time algorithm to find a spanning tree where the leaf set has a property that can be decided in \(f(n)\) time and has minimum or maximum size.
@article{casel2020cliquy, abstract = {An independency (cliquy) tree of an \(n\)-vertex graph \(G\) is a spanning tree of \(G\) in which the set of leaves induces an independent set (clique). We study the problems of minimizing or maximizing the number of leaves of such trees, and fully characterize their parameterized complexity. We show that all four variants of deciding if an independency/cliquy tree with at least/most \(\ell\) leaves exists parameterized by \(\ell\) are either para-NP- or W[1]-hard. We prove that minimizing the number of leaves of a cliquy tree parameterized by the number of internal vertices is para-NP-hard too. However, we show that minimizing the number of leaves of an independency tree parameterized by the number \(k\) of internal vertices has an \(O^*(4^k)\)-time algorithm and a \(2k\) vertex kernel. Moreover, we prove that maximizing the number of leaves of an independency/cliquy tree parameterized by the number \(k\) of internal vertices both have an \(O^*(18^k)\)-time algorithm and an \(O(k\, 2^k)\) vertex kernel, but no polynomial kernel unless the polynomial hierarchy collapses to the third level. Finally, we present an \(O(3^n f(n))\)-time algorithm to find a spanning tree where the leaf set has a property that can be decided in \(f(n)\) time and has minimum or maximum size.}, author = {Casel, Katrin and Dreier, Jan and Fernau, Henning and Gobbert, Moritz and Kuinke, Philipp and Sanchez Villaamil, Fernando and Schmid, Markus L. and van Leeuwen, Erik Jan}, journal = {Discrete Applied Mathematics}, keywords = {erikjanvanleeuwen markuslschmid katrincasel jandreier fernandosanchezvillaamil moritzgobbert philippkuinke dam henningfernau year2020}, pages = {2-15}, title = {Complexity of independency and cliquy trees}, volume = 272, year = 2020 }

Bazgan, Cristina; Brankovic, Ljiljana; Casel, Katrin; Fernau, Henning Domination chain: Characterisation, classical complexity, parameterised complexity and approximabilityDiscrete Applied Mathematics 2020: 23–42
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
We survey the most important results regarding the domination chain parameters, including the characterisation of the domination sequence, complexity of exact and parameterised algorithms, and approximation and inapproximability ratios. We provide a number of new results for the upper and lower irredundance and their complements, and a few results for other domination chain problems. In particular, we analyse the structure of maximum irredundant sets and we provide new bounds on the upper irredundance number. We show several approximability results for upper and lower irredundance and their complements on general graphs; all four problems remain NP-hard even on planar cubic graphs and APX-hard on cubic graphs. Finally, we give some results on everywhere dense graphs, and study some related extension problems.
@article{bazgan2020domination, abstract = {We survey the most important results regarding the domination chain parameters, including the characterisation of the domination sequence, complexity of exact and parameterised algorithms, and approximation and inapproximability ratios. We provide a number of new results for the upper and lower irredundance and their complements, and a few results for other domination chain problems. In particular, we analyse the structure of maximum irredundant sets and we provide new bounds on the upper irredundance number. We show several approximability results for upper and lower irredundance and their complements on general graphs; all four problems remain NP-hard even on planar cubic graphs and APX-hard on cubic graphs. Finally, we give some results on everywhere dense graphs, and study some related extension problems.}, author = {Bazgan, Cristina and Brankovic, Ljiljana and Casel, Katrin and Fernau, Henning}, journal = {Discrete Applied Mathematics}, keywords = {christinabazgan katrincasel ljiljanabrankovic dam henningfernau year2020}, pages = {23-42}, title = {Domination chain: Characterisation, classical complexity, parameterised complexity and approximability}, volume = 280, year = 2020 }

Akbari, Saieed; Reza Maimani, Hamid; Parsaei Majd, Leila; Wanless, Ian M. Zero-sum flows for Steiner systemsDiscrete Mathematics 2020: 112074
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Abstract. Given a \(t-(v, k, \lambda)\) design, \(D = (X, B)\), a zero-sum \(n\)-flow of \(D\) is a map \(f : \mathcal{B longrightarrow pm 1, . . . , pm (n − 1)\}\) such that for any point \(x \in X\), the sum of \(f\) over all blocks incident with \(x\) is zero. For a positive integer \(k\), we find a zero-sum \(k\)-flow for an STS(uw) and for an \(STS(2v + 7)\) for \(v equiv 1 (mod 4)\), if there are \(STS(u)\), \(STS(w)\) and \(STS(v)\) such that the \(STS(u)\) and \(STS(v)\) both have a zero-sum \(k\)-flow. In 2015, it was conjectured that for \(v > 7\) every \(STS(v)\) admits a zero-sum 3-flow. Here, it is shown that many cyclic \(STS(v)\) have a zero-sum 3-flow. Also, we investigate the existence of zero-sum flows for some Steiner quadruple systems.
@article{rezamaimani2020zerosum, abstract = {Abstract. Given a \(t-(v, k, \lambda)\) design, \(D = (X, B)\), a zero-sum \(n\)-flow of \(D\) is a map \(f : \mathcal{B} \longrightarrow \{\pm 1, . . . , \pm (n − 1)\}\) such that for any point \(x \in X\), the sum of \(f\) over all blocks incident with \(x\) is zero. For a positive integer \(k\), we find a zero-sum \(k\)-flow for an STS(uw) and for an \(STS(2v + 7)\) for \(v \equiv 1 (mod 4)\), if there are \(STS(u)\), \(STS(w)\) and \(STS(v)\) such that the \(STS(u)\) and \(STS(v)\) both have a zero-sum \(k\)-flow. In 2015, it was conjectured that for \(v > 7\) every \(STS(v)\) admits a zero-sum 3-flow. Here, it is shown that many cyclic \(STS(v)\) have a zero-sum 3-flow. Also, we investigate the existence of zero-sum flows for some Steiner quadruple systems.}, author = {Akbari, Saieed and Reza Maimani, Hamid and Parsaei Majd, Leila and Wanless, Ian M.}, journal = {Discrete Mathematics}, keywords = {ianmwanless leilaparsaeimajd sys:relevantfor:ae hamidrezamaimani dm saieedakbari year2020}, pages = 112074, title = {Zero-sum flows for Steiner systems}, year = 2020 }

Cseh, Ágnes; Heeger, Klaus The stable marriage problem with ties and restricted edgesDiscrete Optimization 2020: 100571
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
In the stable marriage problem, a set of men and a set of women are given, each of whom has a strictly ordered preference list over the acceptable agents in the opposite class. A matching is called stable if it is not blocked by any pair of agents, who mutually prefer each other to their respective partner. Ties in the preferences allow for three different definitions for a stable matching: weak, strong and super-stability. Besides this, acceptable pairs in the instance can be restricted in their ability of blocking a matching or being part of it, which again generates three categories of restrictions on acceptable pairs. Forced pairs must be in a stable matching, forbidden pairs must not appear in it, and lastly, free pairs cannot block any matching. Our computational complexity study targets the existence of a stable solution for each of the three stability definitions, in the presence of each of the three types of restricted pairs. We solve all cases that were still open. As a byproduct, we also derive that the maximum size weakly stable matching problem is hard even in very dense graphs, which may be of independent interest.
@article{CSEH2020100571, abstract = {In the stable marriage problem, a set of men and a set of women are given, each of whom has a strictly ordered preference list over the acceptable agents in the opposite class. A matching is called stable if it is not blocked by any pair of agents, who mutually prefer each other to their respective partner. Ties in the preferences allow for three different definitions for a stable matching: weak, strong and super-stability. Besides this, acceptable pairs in the instance can be restricted in their ability of blocking a matching or being part of it, which again generates three categories of restrictions on acceptable pairs. Forced pairs must be in a stable matching, forbidden pairs must not appear in it, and lastly, free pairs cannot block any matching. Our computational complexity study targets the existence of a stable solution for each of the three stability definitions, in the presence of each of the three types of restricted pairs. We solve all cases that were still open. As a byproduct, we also derive that the maximum size weakly stable matching problem is hard even in very dense graphs, which may be of independent interest.}, author = {Cseh, Ágnes and Heeger, Klaus}, journal = {Discrete Optimization}, keywords = {sys:relevantfor:ae klausheeger agnescseh do year2020}, pages = 100571, title = {The stable marriage problem with ties and restricted edges}, volume = 36, year = 2020 }

Doerr, Benjamin; Krejca, Martin S. Significance-based Estimation-of-Distribution AlgorithmsIEEE Transactions on Evolutionary Computation 2020: 1025–1034
[ Abstract ] [ BibTeX ] [ DOI ] [ Download ]
 
Estimation-of-distribution algorithms (EDAs) are randomized search heuristics that create a probabilistic model of the solution space, which is updated iteratively, based on the quality of the solutions sampled according to the model. As previous works show, this iteration-based perspective can lead to erratic updates of the model, in particular, to bit-frequencies approaching a random boundary value. In order to overcome this problem, we propose a new EDA based on the classic compact genetic algorithm (cGA) that takes into account a longer history of samples and updates its model only with respect to information which it classifies as statistically significant. We prove that this significance-based compact genetic algorithm (sig-cGA) optimizes the commonly regarded benchmark functions OneMax, LeadingOnes, and BinVal all in quasilinear time, a result shown for no other EDA or evolutionary algorithm so far. For the recently proposed scGA – an EDA that tries to prevent erratic model updates by imposing a bias to the uniformly distributed model – we prove that it optimizes OneMax only in a time exponential in its hypothetical population size. Similarly, we show that the convex search algorithm cannot optimize OneMax in polynomial time.
@article{doerrsignificancebased, abstract = {Estimation-of-distribution algorithms (EDAs) are randomized search heuristics that create a probabilistic model of the solution space, which is updated iteratively, based on the quality of the solutions sampled according to the model. As previous works show, this iteration-based perspective can lead to erratic updates of the model, in particular, to bit-frequencies approaching a random boundary value. In order to overcome this problem, we propose a new EDA based on the classic compact genetic algorithm (cGA) that takes into account a longer history of samples and updates its model only with respect to information which it classifies as statistically significant. We prove that this significance-based compact genetic algorithm (sig-cGA) optimizes the commonly regarded benchmark functions OneMax, LeadingOnes, and BinVal all in quasilinear time, a result shown for no other EDA or evolutionary algorithm so far. For the recently proposed scGA – an EDA that tries to prevent erratic model updates by imposing a bias to the uniformly distributed model – we prove that it optimizes OneMax only in a time exponential in its hypothetical population size. Similarly, we show that the convex search algorithm cannot optimize OneMax in polynomial time.}, author = {Doerr, Benjamin and Krejca, Martin S.}, journal = {IEEE Transactions on Evolutionary Computation}, keywords = {martinskrejca benjamindoerr tevoc year2020}, number = 6, pages = {1025-1034}, publisher = {IEEE}, title = {Significance-based Estimation-of-Distribution Algorithms}, volume = 24, year = 2020 }

Alizadeh, Faezeh; Maimani, Hamid Reza; Parsaei Majd, Leila; Rajabi Parsa, Mina Roman 2-domination in graphs and graph productsIranian Journal of Mathematical Sciences and Informatics Iranian Journal of Mathematical Sciences and Informatics 2020
[ Abstract ] [ BibTeX ] [ Download ]
 
For a graph \(G = (V, E)\) of order n, a Roman 2-dominating function \(f : V \to \0, 1, 2\}\) has the property that for every vertex \(v \in V\) with \(f(v) = 0\), either \(v\) is adjacent to a vertex assigned 2 under \(f\) , or \(v\) is adjacent to at least two vertices assigned 1 under \(f\). In this paper, we classify all graphs with Roman 2-domination number belonging to the set \(\{2, 3, 4, n - 2, n - 1, n\}\). Furthermore, we obtain some results about Roman 2-domination number of some graph operations.
@article{noauthororeditor2020roman, abstract = {For a graph \(G = (V, E)\) of order n, a Roman {2}-dominating function \(f : V \to \{0, 1, 2\}\) has the property that for every vertex \(v \in V\) with \(f(v) = 0\), either \(v\) is adjacent to a vertex assigned 2 under \(f\) , or \(v\) is adjacent to at least two vertices assigned 1 under \(f\). In this paper, we classify all graphs with Roman {2}-domination number belonging to the set \(\{2, 3, 4, n - 2, n - 1, n\}\). Furthermore, we obtain some results about Roman {2}-domination number of some graph operations.}, author = {Alizadeh, Faezeh and Maimani, Hamid Reza and Parsaei Majd, Leila and Rajabi Parsa, Mina}, journal = {Iranian Journal of Mathematical Sciences and Informatics Iranian Journal of Mathematical Sciences and Informatics}, keywords = {leilaparsaeimajd sys:relevantfor:ae hamidrezamaimani faezealizadeh minarajabiparsa year2020}, title = {Roman {2}-domination in graphs and graph products}, year = 2020 }

Bläsius, Thomas; Friedrich, Tobias; Katzmann, Maximilian; Krohmer, Anton Hyperbolic Embeddings for Near-Optimal Greedy RoutingJournal of Experimental Algorithmics (JEA) 2020: 1–18
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Greedy routing computes paths between nodes in a network by successively moving to the neighbor closest to the target with respect to coordinates given by an embedding into some metric space. Its advantage is that only local information is used for routing decisions. We present different algorithms for generating graph embeddings into the hyperbolic plane that are well suited for greedy routing. In particular, our embeddings guarantee that greedy routing always succeeds in reaching the target, and we try to minimize the lengths of the resulting greedy paths. We evaluate our algorithm on multiple generated and real-world networks. For networks that are generally assumed to have a hidden underlying hyperbolic geometry, such as the Internet graph, we achieve near-optimal results (i.e., the resulting greedy paths are only slightly longer than the corresponding shortest paths). In the case of the Internet graph, they are only \(6\%\) longer when using our best algorithm, which greatly improves upon the previous best known embedding, whose creation required substantial manual intervention. In addition to measuring the stretch, we empirically evaluate our algorithms regarding the size of the coordinates of the resulting embeddings and observe how it impacts the success rate when coordinates are not represented with very high precision. Since numerical difficulties are a major issue when performing computations in the hyperbolic plane, we consider variations of our algorithm that improve the success rate when using coordinates with lower precision.
@article{blasius2020hyperbolic, abstract = {Greedy routing computes paths between nodes in a network by successively moving to the neighbor closest to the target with respect to coordinates given by an embedding into some metric space. Its advantage is that only local information is used for routing decisions. We present different algorithms for generating graph embeddings into the hyperbolic plane that are well suited for greedy routing. In particular, our embeddings guarantee that greedy routing always succeeds in reaching the target, and we try to minimize the lengths of the resulting greedy paths. We evaluate our algorithm on multiple generated and real-world networks. For networks that are generally assumed to have a hidden underlying hyperbolic geometry, such as the Internet graph, we achieve near-optimal results (i.e., the resulting greedy paths are only slightly longer than the corresponding shortest paths). In the case of the Internet graph, they are only \(6\%\) longer when using our best algorithm, which greatly improves upon the previous best known embedding, whose creation required substantial manual intervention. In addition to measuring the stretch, we empirically evaluate our algorithms regarding the size of the coordinates of the resulting embeddings and observe how it impacts the success rate when coordinates are not represented with very high precision. Since numerical difficulties are a major issue when performing computations in the hyperbolic plane, we consider variations of our algorithm that improve the success rate when using coordinates with lower precision.}, author = {Bläsius, Thomas and Friedrich, Tobias and Katzmann, Maximilian and Krohmer, Anton}, journal = {Journal of Experimental Algorithmics (JEA)}, keywords = {jea thomasblaesius tobiasfriedrich hyperbolic_embedding antonkrohmer maximiliankatzmann year2020}, month = {March}, number = {1.3}, pages = {1-18}, title = {Hyperbolic Embeddings for Near-Optimal Greedy Routing}, volume = 25, year = 2020 }

Birnick, Johann; Bläsius, Thomas; Friedrich, Tobias; Naumann, Felix; Papenbrock, Thorsten; Schirneck, Martin Hitting Set Enumeration with Partial Information for Unique Column Combination DiscoveryProceedings of the VLDB Endowment 2020: 2270–2283
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Unique column combinations (UCCs) are a fundamental concept in relational databases. They identify entities in the data and support various data management activities. Still, UCCs are usually not explicitly defined and need to be discovered. State-of-the-art data profiling algorithms are able to efficiently discover UCCs in moderately sized datasets, but they tend to fail on large and, in particular, on wide datasets due to run time and memory limitations. In this paper, we introduce HPIValid, a novel UCC discovery algorithm that implements a faster and more resource-saving search strategy. HPIValid models the metadata discovery as a hitting set enumeration problem in hypergraphs. In this way, it combines efficient discovery techniques from data profiling research with the most recent theoretical insights into enumeration algorithms. Our evaluation shows that HPIValid is not only orders of magnitude faster than related work, it also has a much smaller memory footprint.
@article{birnick2020hitting, abstract = {Unique column combinations (UCCs) are a fundamental concept in relational databases. They identify entities in the data and support various data management activities. Still, UCCs are usually not explicitly defined and need to be discovered. State-of-the-art data profiling algorithms are able to efficiently discover UCCs in moderately sized datasets, but they tend to fail on large and, in particular, on wide datasets due to run time and memory limitations. In this paper, we introduce HPIValid, a novel UCC discovery algorithm that implements a faster and more resource-saving search strategy. HPIValid models the metadata discovery as a hitting set enumeration problem in hypergraphs. In this way, it combines efficient discovery techniques from data profiling research with the most recent theoretical insights into enumeration algorithms. Our evaluation shows that HPIValid is not only orders of magnitude faster than related work, it also has a much smaller memory footprint.}, author = {Birnick, Johann and Bläsius, Thomas and Friedrich, Tobias and Naumann, Felix and Papenbrock, Thorsten and Schirneck, Martin}, journal = {Proceedings of the VLDB Endowment}, keywords = {pvldb thomasblaesius johannbirnick tobiasfriedrich thorstenpapenbrock felixnaumann martinschirneck year2020}, number = 11, pages = {2270 - 2283}, title = {Hitting Set Enumeration with Partial Information for Unique Column Combination Discovery}, volume = 13, year = 2020 }

Battaglia, Francesco; Cucina, Domenico; Rizzo, Manuel Parsimonious periodic autoregressive models for time series with evolving trend and seasonalityStatistics and Computing 2020: 77–91
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
This paper proposes an extension of Periodic AutoRegressive (PAR) modelling for time series with evolving features. The large scale of modern datasets, in fact, implies that the time span may subtend several evolving patterns of the underlying series, affecting also seasonality. The proposed model allows several regimes in time and a possibly different PAR process with a trend term in each regime. The means, autocorrelations and residual variances may change both with the regime and the season, resulting in a very large number of parameters. Therefore as a second step we propose a grouping procedure on the PAR parameters, in order to obtain a more parsimonious and concise model. The model selection procedure is a complex combinatorial problem, and it is solved basing on Genetic Algorithms that optimize an information criterion. The model is tested in both simulation studies and real data analysis from different fields, proving to be effective for a wide range of series with evolving features, and competitive with respect to more specific models.
@article{battaglia2019parsimonious, abstract = {This paper proposes an extension of Periodic AutoRegressive (PAR) modelling for time series with evolving features. The large scale of modern datasets, in fact, implies that the time span may subtend several evolving patterns of the underlying series, affecting also seasonality. The proposed model allows several regimes in time and a possibly different PAR process with a trend term in each regime. The means, autocorrelations and residual variances may change both with the regime and the season, resulting in a very large number of parameters. Therefore as a second step we propose a grouping procedure on the PAR parameters, in order to obtain a more parsimonious and concise model. The model selection procedure is a complex combinatorial problem, and it is solved basing on Genetic Algorithms that optimize an information criterion. The model is tested in both simulation studies and real data analysis from different fields, proving to be effective for a wide range of series with evolving features, and competitive with respect to more specific models.}, author = {Battaglia, Francesco and Cucina, Domenico and Rizzo, Manuel}, journal = {Statistics and Computing}, keywords = {sys:relevantfor:ae domenicocucina francescobattaglia manuelrizzo sc year2020}, pages = {77-91}, title = {Parsimonious periodic autoregressive models for time series with evolving trend and seasonality}, volume = 30, year = 2020 }

Friedrich, Tobias; Kötzing, Timo; Lagodzinski, J. A. Gregor; Neumann, Frank; Schirneck, Martin Analysis of the (1+1) EA on Subclasses of Linear Functions under Uniform and Linear ConstraintsTheoretical Computer Science 2020: 3–19
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Linear functions have gained great attention in the run time analysis of evolutionary computation methods. The corresponding investigations have provided many effective tools for analyzing more complex problems. So far, the runtime analysis of evolutionary algorithms has mainly focused on unconstrained problems, but problems occurring in applications frequently involve constraints. Therefore, there is a strong need to extend the methods for analyzing unconstrained problems to a setting involving constraints. In this paper, we consider the behavior of the classical (1+1) evolutionary algorithm on linear functions under linear constraint. We show tight bounds in the case where the constraint is given by the OneMax function and the objective function is given by either the OneMax or the BinVal function. For the general case we present upper and lower bounds.
@article{friedrich2020analysis, abstract = {Linear functions have gained great attention in the run time analysis of evolutionary computation methods. The corresponding investigations have provided many effective tools for analyzing more complex problems. So far, the runtime analysis of evolutionary algorithms has mainly focused on unconstrained problems, but problems occurring in applications frequently involve constraints. Therefore, there is a strong need to extend the methods for analyzing unconstrained problems to a setting involving constraints. In this paper, we consider the behavior of the classical (1+1) evolutionary algorithm on linear functions under linear constraint. We show tight bounds in the case where the constraint is given by the OneMax function and the objective function is given by either the OneMax or the BinVal function. For the general case we present upper and lower bounds.}, author = {Friedrich, Tobias and Kötzing, Timo and Lagodzinski, J. A. Gregor and Neumann, Frank and Schirneck, Martin}, editor = {Oliveto, Pietro S. and Sutton, Andrew M.}, journal = {Theoretical Computer Science}, keywords = {gregorlagodzinski tcs timokoetzing year2018 tobiasfriedrich frankneumann martinschirneck}, pages = {3-19}, title = {Analysis of the (1+1) EA on Subclasses of Linear Functions under Uniform and Linear Constraints}, volume = 832, year = 2020 }

Kötzing, Timo; Lagodzinski, J. A. Gregor; Lengler, Johannes; Melnichenko, Anna Destructiveness of lexicographic parsimony pressure and alleviation by a concatenation crossover in genetic programmingTheoretical Computer Science 2020: 96–113
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
For theoretical analyses there are two specifics distinguishing GP from many other areas of evolutionary computation: the variable size representations, in particular yielding a possible bloat (i.e. the growth of individuals with redundant parts); and also the role and the realization of crossover, which is particularly central in GP due to the tree-based representation. Whereas some theoretical work on GP has studied the effects of bloat, crossover had surprisingly little share in this work. We analyze a simple crossover operator in combination with randomized local search, where a preference for small solutions minimizes bloat (lexicographic parsimony pressure); we denote the resulting algorithm Concatenation Crossover GP. We consider three variants of the well-studied Majority test function, adding large plateaus in different ways to the fitness landscape and thus giving a test bed for analyzing the interplay of variation operators and bloat control mechanisms in a setting with local optima. We show that the Concatenation Crossover GP can efficiently optimize these test functions, while local search cannot be efficient for all three variants independent of employing bloat control.
@article{ktzing2020destructiveness, abstract = {For theoretical analyses there are two specifics distinguishing GP from many other areas of evolutionary computation: the variable size representations, in particular yielding a possible bloat (i.e. the growth of individuals with redundant parts); and also the role and the realization of crossover, which is particularly central in GP due to the tree-based representation. Whereas some theoretical work on GP has studied the effects of bloat, crossover had surprisingly little share in this work. We analyze a simple crossover operator in combination with randomized local search, where a preference for small solutions minimizes bloat (lexicographic parsimony pressure); we denote the resulting algorithm Concatenation Crossover GP. We consider three variants of the well-studied Majority test function, adding large plateaus in different ways to the fitness landscape and thus giving a test bed for analyzing the interplay of variation operators and bloat control mechanisms in a setting with local optima. We show that the Concatenation Crossover GP can efficiently optimize these test functions, while local search cannot be efficient for all three variants independent of employing bloat control.}, author = {Kötzing, Timo and Lagodzinski, J. A. Gregor and Lengler, Johannes and Melnichenko, Anna}, journal = {Theoretical Computer Science}, keywords = {gregorlagodzinski tcs timokoetzing johanneslengler annamelnichenko year2020}, pages = {96&ndash;113}, title = {Destructiveness of lexicographic parsimony pressure and alleviation by a concatenation crossover in genetic programming}, volume = 816, year = 2020 }

Krejca, Martin S.; Witt, Carsten Lower Bounds on the Run Time of the Univariate Marginal Distribution Algorithm on OneMaxTheoretical Computer Science 2020: 143–165
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The Univariate Marginal Distribution Algorithm (UMDA) -- a popular estimation-of-distribution algorithm -- is studied from a run time perspective. On the classical OneMax benchmark function on bit strings of length \(n\), a lower bound of \(\Omega(\lambda + \mu \sqrt{n} + n\log n)\), where \(\mu\) and \(\lambda\) are algorithm-specific parameters, on its expected run time is proved. This is the first direct lower bound on the run time of UMDA. It is stronger than the bounds that follow from general black-box complexity theory and is matched by the run time of many evolutionary algorithms. The results are obtained through advanced analyses of the stochastic change of the frequencies of bit values maintained by the algorithm, including carefully designed potential functions. These techniques may prove useful in advancing the field of run time analysis for estimation-of-distribution algorithms in general.
@article{krejca2020lower, abstract = {The Univariate Marginal Distribution Algorithm (UMDA) &ndash; a popular estimation-of-distribution algorithm &ndash; is studied from a run time perspective. On the classical OneMax benchmark function on bit strings of length \(n\), a lower bound of \(\Omega(\lambda + \mu \sqrt{n} + n\log n)\), where \(\mu\) and \(\lambda\) are algorithm-specific parameters, on its expected run time is proved. This is the first direct lower bound on the run time of UMDA. It is stronger than the bounds that follow from general black-box complexity theory and is matched by the run time of many evolutionary algorithms. The results are obtained through advanced analyses of the stochastic change of the frequencies of bit values maintained by the algorithm, including carefully designed potential functions. These techniques may prove useful in advancing the field of run time analysis for estimation-of-distribution algorithms in general.}, author = {Krejca, Martin S. and Witt, Carsten}, journal = {Theoretical Computer Science}, keywords = {tcs martinskrejca carstenwitt year2020}, pages = {143-165}, title = {Lower Bounds on the Run Time of the Univariate Marginal Distribution Algorithm on OneMax}, volume = 832, year = 2020 }

Doerr, Benjamin; Kötzing, Timo; Lagodzinski, J. A. Gregor; Lengler, Johannes The impact of lexicographic parsimony pressure for ORDER/MAJORITY on the run timeTheoretical Computer Science 2020: 144–168
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
While many optimization problems work with a fixed number of decision variables and thus a fixed-length representation of possible solutions, genetic programming (GP) works on variable-length representations. A naturally occurring problem is that of bloat, that is, the unnecessary growth of solution lengths, which may slow down the optimization process. So far, the mathematical runtime analysis could not deal well with bloat and required explicit assumptions limiting bloat. In this paper, we provide the first mathematical runtime analysis of a GP algorithm that does not require any assumptions on the bloat. Previous performance guarantees were only proven conditionally for runs in which no strong bloat occurs. Together with improved analyses for the case with bloat restrictions our results show that such assumptions on the bloat are not necessary and that the algorithm is efficient without explicit bloat control mechanism. More specifically, we analyzed the performance of the \((1+1)\) GP on the two benchmark functions Order and Majority. When using lexicographic parsimony pressure as bloat control, we show a tight runtime estimate of \(O(T_{init+n \log n)\) iterations both for Order and Majority. For the case without bloat control, the bounds \(O(T_{init log T_init + n (\log n)^3)\) and \(\Omega(T_init + n \log n)\) (and \(Omega (T_init + \log T_{init})\) for \(n=1\)) hold for Majority.
@article{doerr2020impact, abstract = {While many optimization problems work with a fixed number of decision variables and thus a fixed-length representation of possible solutions, genetic programming (GP) works on variable-length representations. A naturally occurring problem is that of bloat, that is, the unnecessary growth of solution lengths, which may slow down the optimization process. So far, the mathematical runtime analysis could not deal well with bloat and required explicit assumptions limiting bloat. In this paper, we provide the first mathematical runtime analysis of a GP algorithm that does not require any assumptions on the bloat. Previous performance guarantees were only proven conditionally for runs in which no strong bloat occurs. Together with improved analyses for the case with bloat restrictions our results show that such assumptions on the bloat are not necessary and that the algorithm is efficient without explicit bloat control mechanism. More specifically, we analyzed the performance of the \((1+1)\) GP on the two benchmark functions Order and Majority. When using lexicographic parsimony pressure as bloat control, we show a tight runtime estimate of \(O(T_{init}+n \log n)\) iterations both for Order and Majority. For the case without bloat control, the bounds \(O(T_{init} \log T_{init} + n (\log n)^3)\) and \(\Omega(T_{init} + n \log n)\) (and \(\Omega (T_{init} + \log T_{init})\) for \(n=1\)) hold for Majority.}, author = {Doerr, Benjamin and Kötzing, Timo and Lagodzinski, J. A. Gregor and Lengler, Johannes}, journal = {Theoretical Computer Science}, keywords = {gregorlagodzinski tcs timokoetzing johanneslengler benjamindoerr year2020}, pages = {144&ndash;168}, title = {The impact of lexicographic parsimony pressure for ORDER/MAJORITY on the run time}, volume = 816, year = 2020 }

Bilò, Davide; Lenzner, Pascal On the Tree Conjecture for the Network Creation GameTheory of Computing Systems 2020: 422–443
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Selfish Network Creation focuses on modeling real world networks from a game-theoretic point of view. One of the classic models by Fabrikant et al. (2003) is the network creation game, where agents correspond to nodes in a network which buy incident edges for the price of \($\alpha$\) per edge to minimize their total distance to all other nodes. The model is well-studied but still has intriguing open problems. The most famous conjectures state that the price of anarchy is constant for all \($\alpha$\) and that for \($\alpha \geq n$\) all equilibrium networks are trees. We introduce a novel technique for analyzing stable networks for high edge-price \($\alpha$\) and employ it to improve on the best known bound for the latter conjecture. In particular we show that for \($\alpha>4n −13$\) all equilibrium networks must be trees, which implies a constant price of anarchy for this range of \($\alpha$\). Moreover, we also improve the constant upper bound on the price of anarchy for equilibrium trees.
@article{bilo2020conjecture, abstract = {Selfish Network Creation focuses on modeling real world networks from a game-theoretic point of view. One of the classic models by Fabrikant et al. (2003) is the network creation game, where agents correspond to nodes in a network which buy incident edges for the price of $\alpha$ per edge to minimize their total distance to all other nodes. The model is well-studied but still has intriguing open problems. The most famous conjectures state that the price of anarchy is constant for all $\alpha$ and that for $\alpha \geq n$ all equilibrium networks are trees. We introduce a novel technique for analyzing stable networks for high edge-price $\alpha$ and employ it to improve on the best known bound for the latter conjecture. In particular we show that for $\alpha>4n −13$ all equilibrium networks must be trees, which implies a constant price of anarchy for this range of $\alpha$. Moreover, we also improve the constant upper bound on the price of anarchy for equilibrium trees.}, author = {Bil{ò}, Davide and Lenzner, Pascal}, journal = {Theory of Computing Systems}, keywords = {TOCS pascallenzner year2020}, number = 3, pages = {422&ndash;443}, title = {On the Tree Conjecture for the Network Creation Game}, volume = 64, year = 2020 }

Krejca, Martin S.; Witt, Carsten Theory of Estimation-of-Distribution AlgorithmsTheory of Evolutionary Computation: Recent Developments in Discrete Optimization 2020: 405–442
[ Abstract ] [ BibTeX ] [ DOI ] [ Download ]
 
Estimation-of-distribution algorithms (EDAs) are general metaheuristics used in optimization that represent a more recent alternative to classical approaches such as evolutionary algorithms. In a nutshell, EDAs typically do not directly evolve populations of search points but build probabilistic models of promising solutions by repeatedly sampling and selecting points from the underlying search space. Recently, significant progress has been made in the theoretical understanding of EDAs. This chapter provides an up-to-date overview of the most commonly analyzed EDAs and the most recent theoretical results in this area. In particular, emphasis is put on the runtime analysis of simple univariate EDAs, including a description of typical benchmark functions and tools for the analysis. Along the way, open problems and directions for future research are described.
@incollection{krejca2020theory, abstract = {Estimation-of-distribution algorithms (EDAs) are general metaheuristics used in optimization that represent a more recent alternative to classical approaches such as evolutionary algorithms. In a nutshell, EDAs typically do not directly evolve populations of search points but build probabilistic models of promising solutions by repeatedly sampling and selecting points from the underlying search space. Recently, significant progress has been made in the theoretical understanding of EDAs. This chapter provides an up-to-date overview of the most commonly analyzed EDAs and the most recent theoretical results in this area. In particular, emphasis is put on the runtime analysis of simple univariate EDAs, including a description of typical benchmark functions and tools for the analysis. Along the way, open problems and directions for future research are described.}, author = {Krejca, Martin S. and Witt, Carsten}, booktitle = {Theory of Evolutionary Computation: Recent Developments in Discrete Optimization}, chapter = 9, editor = {Doerr, Benjamin and Neumann, Frank}, keywords = {sys:relevantfor:ae martinskrejca carstenwitt year2020}, pages = {405-442}, publisher = {Springer}, series = {Natural Computing Series}, title = {Theory of Estimation-of-Distribution Algorithms}, year = 2020 }

Doskoč, Vanja; Kötzing, Timo Cautious Limit LearningAlgorithmic Learning Theory (ALT) 2020: 251–276
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We investigate language learning in the limit from text with various \(\mathit{cautious}\) learning restrictions. Learning is \(\mathit{cautious}\) if no hypothesis is a proper subset of a previous guess. While dealing with a seemingly natural learning behaviour, cautious learning does severely restrict explanatory (syntactic) learning power. To further understand why exactly this loss of learning power arises, Kötzing and Palenta (2016) introduced weakened versions of cautious learning and gave first partial results on their relation. In this paper, we aim to understand the restriction of cautious learning more fully. To this end we compare the known variants in a number of different settings, namely full-information and (partially) set-driven learning, paired either with the syntactic convergence restriction (explanatory learning) or the semantic convergence restriction (behaviourally correct learning). To do so, we make use of normal forms presented in Kötzing et al. (2017), most notably strongly locking and consistent learning. While strongly locking learners have been exploited when dealing with a variety of syntactic learning restrictions, we show how they can be beneficial in the semantic case as well. Furthermore, we expand the normal forms to a broader range of learning restrictions, including an answer to the open question of whether cautious learners can be assumed to be consistent, as stated in Kötzing et al. (2017).
@inproceedings{doskoc2020cautious, abstract = {We investigate language learning in the limit from text with various \(\mathit{cautious}\) learning restrictions. Learning is \(\mathit{cautious}\) if no hypothesis is a proper subset of a previous guess. While dealing with a seemingly natural learning behaviour, cautious learning does severely restrict explanatory (syntactic) learning power. To further understand why exactly this loss of learning power arises, Kötzing and Palenta (2016) introduced weakened versions of cautious learning and gave first partial results on their relation. In this paper, we aim to understand the restriction of cautious learning more fully. To this end we compare the known variants in a number of different settings, namely full-information and (partially) set-driven learning, paired either with the syntactic convergence restriction (explanatory learning) or the semantic convergence restriction (behaviourally correct learning). To do so, we make use of normal forms presented in Kötzing et al. (2017), most notably strongly locking and consistent learning. While strongly locking learners have been exploited when dealing with a variety of syntactic learning restrictions, we show how they can be beneficial in the semantic case as well. Furthermore, we expand the normal forms to a broader range of learning restrictions, including an answer to the open question of whether cautious learners can be assumed to be consistent, as stated in Kötzing et al. (2017).}, author = {Doskoč, Vanja and Kötzing, Timo}, booktitle = {Algorithmic Learning Theory (ALT)}, keywords = {vanjadoskoc timokoetzing alt year2020}, pages = {251-276}, title = {Cautious Limit Learning}, year = 2020 }

Das, Syamantak; Jain, Lavina; Kumar, Nikhil A Constant Factor Approximation for Capacitated Min-Max Tree CoverApproximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM) 2020: 55:1–55:13
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Given a graph \(G=(V,E)\) with non-negative real edge lengths and an integer parameter \(k\), the (uncapacitated) Min-Max Tree Cover problem seeks to find a set of at most \(k\) trees which together span \(V\) and each tree is a subgraph of \(G\). The objective is to minimize the maximum length among all the trees. In this paper, we consider a capacitated generalization of the above and give the first constant factor approximation algorithm. In the capacitated version, there is a hard uniform capacity (\(\lambda\)) on the number of vertices a tree can cover. Our result extends to the rooted version of the problem, where we are given a set of \(k\) root vertices, \(R\) and each of the covering trees is required to include a distinct vertex in \(R\) as the root. Prior to our work, the only result known was a \((2k-1)\)-approximation algorithm for the special case when the total number of vertices in the graph is \(k\lambda\) [Guttmann-Beck and Hassin, J. of Algorithms, 1997]. Our technique circumvents the difficulty of using the minimum spanning tree of the graph as a lower bound, which is standard for the uncapacitated version of the problem [Even et al., OR Letters 2004],[Khani et al., Algorithmica 2010]. Instead, we use Steiner trees that cover \(\lambda\) vertices along with an iterative refinement procedure that ensures that the output trees have low cost and the vertices are well distributed among the trees.
@inproceedings{das2020constant, abstract = {Given a graph \(G=(V,E)\) with non-negative real edge lengths and an integer parameter \(k\), the (uncapacitated) Min-Max Tree Cover problem seeks to find a set of at most \(k\) trees which together span \(V\) and each tree is a subgraph of \(G\). The objective is to minimize the maximum length among all the trees. In this paper, we consider a capacitated generalization of the above and give the first constant factor approximation algorithm. In the capacitated version, there is a hard uniform capacity (\(\lambda\)) on the number of vertices a tree can cover. Our result extends to the rooted version of the problem, where we are given a set of \(k\) root vertices, \(R\) and each of the covering trees is required to include a distinct vertex in \(R\) as the root. Prior to our work, the only result known was a \((2k-1)\)-approximation algorithm for the special case when the total number of vertices in the graph is \(k\lambda\) [Guttmann-Beck and Hassin, J. of Algorithms, 1997]. Our technique circumvents the difficulty of using the minimum spanning tree of the graph as a lower bound, which is standard for the uncapacitated version of the problem [Even et al., OR Letters 2004],[Khani et al., Algorithmica 2010]. Instead, we use Steiner trees that cover \(\lambda\) vertices along with an iterative refinement procedure that ensures that the output trees have low cost and the vertices are well distributed among the trees.}, author = {Das, Syamantak and Jain, Lavina and Kumar, Nikhil}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM)}, keywords = {syamantakdas nikhilkumar lavinajain approx year2020}, pages = {55:1-55:13}, title = {A Constant Factor Approximation for Capacitated Min-Max Tree Cover}, volume = 176, year = 2020 }

Bläsius, Thomas; Böther, Maximilian; Fischbeck, Philipp; Friedrich, Tobias; Gries, Alina; Hüffner, Falk; Kißig, Otto; Lenzner, Pascal; Molitor, Louise; Schiller, Leon; Wells, Armin; Wietheger, Simon A Strategic Routing Framework and Algorithms for Computing Alternative PathsAlgorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS) 2020: 10:1–10:14
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Traditional navigation services find the fastest route for a single driver. Though always using the fastest route seems desirable for every individual, selfish behavior can have undesirable effects such as higher energy consumption and avoidable congestion, even leading to higher overall and individual travel times. In contrast, strategic routing aims at optimizing the traffic for all agents regarding a global optimization goal. We introduce a framework to formalize real-world strategic routing scenarios as algorithmic problems and study one of them, which we call Single Alternative Path (SAP), in detail. There, we are given an original route between a single origin–destination pair. The goal is to suggest an alternative route to all agents that optimizes the overall travel time under the assumption that the agents distribute among both routes according to a psychological model, for which we introduce the concept of Pareto-conformity. We show that the SAP problem is NP-complete, even for such models. Nonetheless, assuming Pareto-conformity, we give multiple algorithms for different variants of SAP, using multi-criteria shortest path algorithms as subroutines.Moreover, we prove that several natural models are in fact Pareto-conform. The implementation and evaluation of our algorithms serve as a proof of concept, showing that SAP can be solved in reasonable time even though the algorithms have exponential running time in the worst case.
@inproceedings{blasius2020strategic, abstract = {Traditional navigation services find the fastest route for a single driver. Though always using the fastest route seems desirable for every individual, selfish behavior can have undesirable effects such as higher energy consumption and avoidable congestion, even leading to higher overall and individual travel times. In contrast, strategic routing aims at optimizing the traffic for all agents regarding a global optimization goal. We introduce a framework to formalize real-world strategic routing scenarios as algorithmic problems and study one of them, which we call Single Alternative Path (SAP), in detail. There, we are given an original route between a single origin–destination pair. The goal is to suggest an alternative route to all agents that optimizes the overall travel time under the assumption that the agents distribute among both routes according to a psychological model, for which we introduce the concept of Pareto-conformity. We show that the SAP problem is NP-complete, even for such models. Nonetheless, assuming Pareto-conformity, we give multiple algorithms for different variants of SAP, using multi-criteria shortest path algorithms as subroutines.Moreover, we prove that several natural models are in fact Pareto-conform. The implementation and evaluation of our algorithms serve as a proof of concept, showing that SAP can be solved in reasonable time even though the algorithms have exponential running time in the worst case.}, author = {Bläsius, Thomas and Böther, Maximilian and Fischbeck, Philipp and Friedrich, Tobias and Gries, Alina and Hüffner, Falk and Kißig, Otto and Lenzner, Pascal and Molitor, Louise and Schiller, Leon and Wells, Armin and Wietheger, Simon}, booktitle = {Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS)}, keywords = {maximilianboether falkhueffner tobiasfriedrich simonwietheger arminwells atmos ottokissig sys:relevantfor:ae philippfischbeck thomasblaesius louisemolitor alinagries leonschiller pascallenzner year2020}, pages = {10:1&ndash;10:14}, title = {A Strategic Routing Framework and Algorithms for Computing Alternative Paths}, volume = 85, year = 2020 }

Fogel, Sharon; Averbuch-Elor, Hadar; Cohen, Sarel; Mazor, Shai; Litman, Roee ScrabbleGAN: Semi-Supervised Varying Length Handwritten Text GenerationConference on Computer Vision and Pattern Recognition (CVPR) 2020: 4323–4332
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Optical character recognition (OCR) systems performance have improved significantly in the deep learning era. This is especially true for handwritten text recognition (HTR), where each author has a unique style, unlike printed text, where the variation is smaller by design. That said, deep learning based HTR is limited, as in every other task, by the number of training examples. Gathering data is a challenging and costly task, and even more so, the labeling task that follows, of which we focus here. One possible approach to reduce the burden of data annotation is semi-supervised learning. Semi supervised methods use, in addition to labeled data, some unlabeled samples to improve performance, compared to fully supervised ones. Consequently, such methods may adapt to unseen images during test time. We present ScrabbleGAN, a semi-supervised approach to synthesize handwritten text images that are versatile both in style and lexicon. ScrabbleGAN relies on a novel generative model which can generate images of words with an arbitrary length. We show how to operate our approach in a semi-supervised manner, enjoying the aforementioned benefits such as performance boost over state of the art supervised HTR. Furthermore, our generator can manipulate the resulting text style. This allows us to change, for instance, whether the text is cursive, or how thin is the pen stroke.
@inproceedings{fogel2020scrabblegan, abstract = {Optical character recognition (OCR) systems performance have improved significantly in the deep learning era. This is especially true for handwritten text recognition (HTR), where each author has a unique style, unlike printed text, where the variation is smaller by design. That said, deep learning based HTR is limited, as in every other task, by the number of training examples. Gathering data is a challenging and costly task, and even more so, the labeling task that follows, of which we focus here. One possible approach to reduce the burden of data annotation is semi-supervised learning. Semi supervised methods use, in addition to labeled data, some unlabeled samples to improve performance, compared to fully supervised ones. Consequently, such methods may adapt to unseen images during test time. We present ScrabbleGAN, a semi-supervised approach to synthesize handwritten text images that are versatile both in style and lexicon. ScrabbleGAN relies on a novel generative model which can generate images of words with an arbitrary length. We show how to operate our approach in a semi-supervised manner, enjoying the aforementioned benefits such as performance boost over state of the art supervised HTR. Furthermore, our generator can manipulate the resulting text style. This allows us to change, for instance, whether the text is cursive, or how thin is the pen stroke.}, author = {Fogel, Sharon and Averbuch-Elor, Hadar and Cohen, Sarel and Mazor, Shai and Litman, Roee}, booktitle = {Conference on Computer Vision and Pattern Recognition (CVPR)}, keywords = {sarelcohen sys:relevantfor:ae shaimazor roeelitman cvpr sharonfogel hadaraverbuch-elor year2020}, pages = {4323-4332}, title = {ScrabbleGAN: Semi-Supervised Varying Length Handwritten Text Generation}, year = 2020 }

Doskoč, Vanja; Friedrich, Tobias; Göbel, Andreas; Neumann, Aneta; Neumann, Frank; Quinzan, Francesco Non-Monotone Submodular Maximization with Multiple Knapsacks in Static and Dynamic SettingsEuropean Conference on Artificial Intelligence (ECAI) 2020: 435–442
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We study the problem of maximizing a non-monotone submodular function under multiple knapsack constraints. We propose a simple discrete greedy algorithm to approach this problem, and prove that it yields strong approximation guarantees for functions with bounded curvature. In contrast to other heuristics, this does not require problem relaxation to continuous domains and it maintains a constant-factor approximation guarantee in the problem size. In the case of a single knapsack, our analysis suggests that the standard greedy can be used in non-monotone settings. Additionally, we study this problem in a dynamic setting, in which knapsacks change during the optimization process. We modify our greedy algorithm to avoid a complete restart at each constraint update. This modification retains the approximation guarantees of the static case. We evaluate our results experimentally on a video summarization and sensor placement task. We show that our proposed algorithm competes with the state-of-the-art in static settings. Furthermore, we show that in dynamic settings with tight computational time budget, our modified greedy yields significant improvements over starting the greedy from scratch, in terms of the solution quality achieved.
@inproceedings{doskoc2020nonmonotone, abstract = {We study the problem of maximizing a non-monotone submodular function under multiple knapsack constraints. We propose a simple discrete greedy algorithm to approach this problem, and prove that it yields strong approximation guarantees for functions with bounded curvature. In contrast to other heuristics, this does not require problem relaxation to continuous domains and it maintains a constant-factor approximation guarantee in the problem size. In the case of a single knapsack, our analysis suggests that the standard greedy can be used in non-monotone settings. Additionally, we study this problem in a dynamic setting, in which knapsacks change during the optimization process. We modify our greedy algorithm to avoid a complete restart at each constraint update. This modification retains the approximation guarantees of the static case. We evaluate our results experimentally on a video summarization and sensor placement task. We show that our proposed algorithm competes with the state-of-the-art in static settings. Furthermore, we show that in dynamic settings with tight computational time budget, our modified greedy yields significant improvements over starting the greedy from scratch, in terms of the solution quality achieved.}, author = {Doskoč, Vanja and Friedrich, Tobias and Göbel, Andreas and Neumann, Aneta and Neumann, Frank and Quinzan, Francesco}, booktitle = {European Conference on Artificial Intelligence (ECAI)}, keywords = {anetaneumann vanjadoskoc andreasgoebel francescoquinzan tobiasfriedrich ecai frankneumann year2020}, pages = {435-442}, publisher = {{IOS} Press}, title = {Non-Monotone Submodular Maximization with Multiple Knapsacks in Static and Dynamic Settings}, year = 2020 }

Bläsius, Thomas; Friedrich, Tobias; Schirneck, Martin The Minimization of Random HypergraphsEuropean Symposium on Algorithms (ESA) 2020: 21:1–21:15
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We investigate the maximum-entropy model \(\mathcal{B}_{n,m,p}\) for random \(n\)-vertex, \(m\)-edge multi-hypergraphs with expected edge size \(pn\). We show that the expected size of the minimization \(\min(\mathcal{B}_{n,m,p})\), i.e., the number of inclusion-wise minimal edges of \(\mathcal{B}_{n,m,p}\), undergoes a phase transition with respect to \(m\). If \(m\) is at most \(1/(1-p)^(1-p)n}\), then \(\mathrm{E[|\min(\mathcal{B}_{n,m,p})|]\) is of order \(\Theta(m)\), while for \(m ge 1/(1-p)^(1-p+\varepsilon)n}\) for any \(\varepsilon > 0\), it is \(\Theta( 2^(\mathrm{H(\alpha) + (1-\alpha) \log_2 p) n/ \sqrt{n})\). Here, \(\mathrm{H}\) denotes the binary entropy function and \(alpha = - (\log_{1-p m)/n\). The result implies that the maximum expected number of minimal edges over all \(m\) is \(\Theta((1+p)^n/\sqrt{n})\). Our structural findings have algorithmic implications for minimizing an input hypergraph. This has applications in the profiling of relational databases as well as for the Orthogonal Vectors problem studied in fine-grained complexity. We make several technical contributions that are of independent interest in probability. First, we improve the Chernoff--Hoeffding theorem on the tail of the binomial distribution. In detail, we show that for a binomial variable \(Y sim \mathrm{Bin(n,p)\) and any \(0 < x < p\), it holds that \(\mathrm{P[Y le xn] = \Theta( 2^-\!\mathrm{D(x \,\|}\, p) n}/\sqrt{n})\), where \(\mathrm{D}\) is the binary Kullback--Leibler divergence between Bernoulli distributions. We give explicit upper and lower bounds on the constants hidden in the big-O notation that hold for all \(n\). Secondly, we establish the fact that the probability of a set of cardinality \(i\) being minimal after \(m\) i.i.d. maximum-entropy trials exhibits a sharp threshold behavior at \(i^* = n + \log_{1-p m\).
@inproceedings{Blaesius20MinimizationESA, abstract = {We investigate the maximum-entropy model \(\mathcal{B}_{n,m,p}\) for random \(n\)-vertex, \(m\)-edge multi-hypergraphs with expected edge size \(pn\). We show that the expected size of the minimization \(\min(\mathcal{B}_{n,m,p})\), i.e., the number of inclusion-wise minimal edges of \(\mathcal{B}_{n,m,p}\), undergoes a phase transition with respect to \(m\). If \(m\) is at most \(1/(1-p)^{(1-p)n}\), then \(\mathrm{E}[|\min(\mathcal{B}_{n,m,p})|]\) is of order \(\Theta(m)\), while for \(m \ge 1/(1-p)^{(1-p+\varepsilon)n}\) for any \(\varepsilon > 0\), it is \(\Theta( 2^{(\mathrm{H}(\alpha) + (1-\alpha) \log_2 p) n}/ \sqrt{n})\). Here, \(\mathrm{H}\) denotes the binary entropy function and \(\alpha = - (\log_{1-p} m)/n\). The result implies that the maximum expected number of minimal edges over all \(m\) is \(\Theta((1+p)^n/\sqrt{n})\). Our structural findings have algorithmic implications for minimizing an input hypergraph. This has applications in the profiling of relational databases as well as for the Orthogonal Vectors problem studied in fine-grained complexity. We make several technical contributions that are of independent interest in probability. First, we improve the Chernoff&ndash;Hoeffding theorem on the tail of the binomial distribution. In detail, we show that for a binomial variable \(Y \sim \mathrm{Bin}(n,p)\) and any \(0 < x < p\), it holds that \(\mathrm{P}[Y \le xn] = \Theta( 2^{-\!\mathrm{D}(x \,{\|}\, p) n}/\sqrt{n})\), where \(\mathrm{D}\) is the binary Kullback&ndash;Leibler divergence between Bernoulli distributions. We give explicit upper and lower bounds on the constants hidden in the big-O notation that hold for all \(n\). Secondly, we establish the fact that the probability of a set of cardinality \(i\) being minimal after \(m\) i.i.d. maximum-entropy trials exhibits a sharp threshold behavior at \(i^* = n + \log_{1-p} m\).}, author = {Bläsius, Thomas and Friedrich, Tobias and Schirneck, Martin}, booktitle = {European Symposium on Algorithms (ESA)}, keywords = {esa thomasblaesius tobiasfriedrich martinschirneck year2020}, pages = {21:1-21:15}, title = {The Minimization of Random Hypergraphs}, year = 2020 }

Garg, Naveen; Kumar, Nikhil Dual Half-Integrality for Uncrossable Cut Cover and Its Application to Maximum Half-Integral FlowEuropean Symposium on Algorithms (ESA) 2020: 55:1–55:13
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Given an edge weighted graph and a forest \(F\), the em 2-edge connectivity augmentation problem is to pick a minimum weighted set of edges, \(E'\), such that every connected component of \(E'\cup F\) is 2-edge connected. Williamson et al. gave a 2-approximation algorithm (WGMV) for this problem using the primal-dual schema. We show that when edge weights are integral, the WGMV procedure can be modified to obtain a half-integral dual. The 2-edge connectivity augmentation problem has an interesting connection to routing flow in graphs where the union of supply and demand is planar. The half-integrality of the dual leads to a tight 2-approximate max-half-integral-flow min-multicut theorem.
@inproceedings{garg2020halfintegrality, abstract = {Given an edge weighted graph and a forest \(F\), the {\em 2-edge connectivity augmentation problem} is to pick a minimum weighted set of edges, \(E'\), such that every connected component of \(E'\cup F\) is 2-edge connected. Williamson et al. gave a 2-approximation algorithm (WGMV) for this problem using the primal-dual schema. We show that when edge weights are integral, the WGMV procedure can be modified to obtain a half-integral dual. The 2-edge connectivity augmentation problem has an interesting connection to routing flow in graphs where the union of supply and demand is planar. The half-integrality of the dual leads to a tight 2-approximate max-half-integral-flow min-multicut theorem.}, author = {Garg, Naveen and Kumar, Nikhil}, booktitle = {European Symposium on Algorithms (ESA)}, keywords = {esa nikhilkumar naveengarg year2020}, pages = {55:1-55:13}, title = {Dual Half-Integrality for Uncrossable Cut Cover and Its Application to Maximum Half-Integral Flow}, volume = 173, year = 2020 }

Doerr, Benjamin; Krejca, Martin S. The Univariate Marginal Distribution Algorithm Copes Well With Deception and EpistasisEvolutionary Computation in Combinatorial Optimisation (EvoCOP) 2020: 51–66
Best-Paper Award
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In their recent work, Lehre and Nguyen (FOGA 2019) show that the univariate marginal distribution algorithm (UMDA) needs time exponential in the parent populations size to optimize the DeceivingLeadingBlocks (DLB) problem. They conclude from this result that univariate EDAs have difficulties with deception and epistasis. In this work, we show that this negative finding is caused by an unfortunate choice of the parameters of the UMDA. When the population sizes are chosen large enough to prevent genetic drift, then the UMDA optimizes the DLB problem with high probability with at most \(\lambda(\frac{n}{2 + 2 e \ln n)\) fitness evaluations. Since an offspring population size \(\lambda\) of order \(n \log n\) can prevent genetic drift, the UMDA can solve the DLB problem with \(O(n^2 \log n)\) fitness evaluations. In contrast, for classic evolutionary algorithms no better run time guarantee than \(O(n^3)\) is known, so our result rather suggests that the UMDA can cope well with deception and epistatis. Together with the result of Lehre and Nguyen, our result for the first time rigorously proves that running EDAs in the regime with genetic drift can lead to drastic performance losses.
@inproceedings{doerr2020univariate, abstract = {In their recent work, Lehre and Nguyen (FOGA 2019) show that the univariate marginal distribution algorithm (UMDA) needs time exponential in the parent populations size to optimize the DeceivingLeadingBlocks (DLB) problem. They conclude from this result that univariate EDAs have difficulties with deception and epistasis. In this work, we show that this negative finding is caused by an unfortunate choice of the parameters of the UMDA. When the population sizes are chosen large enough to prevent genetic drift, then the UMDA optimizes the DLB problem with high probability with at most \(\lambda(\frac{n}{2} + 2 e \ln n)\) fitness evaluations. Since an offspring population size \(\lambda\) of order \(n \log n\) can prevent genetic drift, the UMDA can solve the DLB problem with \(O(n^2 \log n)\) fitness evaluations. In contrast, for classic evolutionary algorithms no better run time guarantee than \(O(n^3)\) is known, so our result rather suggests that the UMDA can cope well with deception and epistatis. Together with the result of Lehre and Nguyen, our result for the first time rigorously proves that running EDAs in the regime with genetic drift can lead to drastic performance losses.}, author = {Doerr, Benjamin and Krejca, Martin S.}, booktitle = {Evolutionary Computation in Combinatorial Optimisation (EvoCOP)}, keywords = {martinskrejca evocop benjamindoerr year2020}, note = {Best-Paper Award}, pages = {51-66}, publisher = {Springer}, title = {The Univariate Marginal Distribution Algorithm Copes Well With Deception and Epistasis}, year = 2020 }

Bilò, Davide; Friedrich, Tobias; Lenzner, Pascal; Melnichenko, Anna; Molitor, Louise Fair Tree Connection Games with Topology-Dependent Edge CostFoundations of Software Technology and Theoretical Computer Science (FSTTCS) 2020: 15:1–15:15
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How do rational agents self-organize when trying to connect to a common target? We study this question with a simple tree formation game which is related to the well-known fair single-source connection game by Anshelevich et al.(FOCS'04) and selfish spanning tree games by Gourvès and Monnot (WINE'08). In our game agents correspond to nodes in a network that activate a single outgoing edge to connect to the common target node (possibly via other nodes). Agents pay for their path to the common target, and edge costs are shared fairly among all agents using an edge. The main novelty of our model is dynamic edge costs that depend on the in-degree of the respective endpoint. This reflects that connecting to popular nodes that have increased internal coordination costs is more expensive since they can charge higher prices for their routing service. In contrast to related models, we show that equilibria are not guaranteed to exist, but we prove the existence for infinitely many numbers of agents. Moreover, we analyze the structure of equilibrium trees and employ these insights to prove a constant upper bound on the Price of Anarchy as well as non-trivial lower bounds on both the Price of Anarchy and the Price of Stability. We also show that in comparison with the social optimum tree the overall cost of an equilibrium tree is more fairly shared among the agents. Thus, we prove that self-organization of rational agents yields on average only slightly higher cost per agent compared to the centralized optimum, and at the same time, it induces a more fair cost distribution. Moreover, equilibrium trees achieve a beneficial trade-off between a low height and low maximum degree, and hence these trees might be of independent interest from a combinatorics point-of-view. We conclude with a discussion of promising extensions of our model.
@inproceedings{bilo2020connection, abstract = {How do rational agents self-organize when trying to connect to a common target? We study this question with a simple tree formation game which is related to the well-known fair single-source connection game by Anshelevich et al.(FOCS'04) and selfish spanning tree games by Gourvès and Monnot (WINE'08). In our game agents correspond to nodes in a network that activate a single outgoing edge to connect to the common target node (possibly via other nodes). Agents pay for their path to the common target, and edge costs are shared fairly among all agents using an edge. The main novelty of our model is dynamic edge costs that depend on the in-degree of the respective endpoint. This reflects that connecting to popular nodes that have increased internal coordination costs is more expensive since they can charge higher prices for their routing service. In contrast to related models, we show that equilibria are not guaranteed to exist, but we prove the existence for infinitely many numbers of agents. Moreover, we analyze the structure of equilibrium trees and employ these insights to prove a constant upper bound on the Price of Anarchy as well as non-trivial lower bounds on both the Price of Anarchy and the Price of Stability. We also show that in comparison with the social optimum tree the overall cost of an equilibrium tree is more fairly shared among the agents. Thus, we prove that self-organization of rational agents yields on average only slightly higher cost per agent compared to the centralized optimum, and at the same time, it induces a more fair cost distribution. Moreover, equilibrium trees achieve a beneficial trade-off between a low height and low maximum degree, and hence these trees might be of independent interest from a combinatorics point-of-view. We conclude with a discussion of promising extensions of our model.}, author = {Bilò, Davide and Friedrich, Tobias and Lenzner, Pascal and Melnichenko, Anna and Molitor, Louise}, booktitle = {Foundations of Software Technology and Theoretical Computer Science (FSTTCS)}, keywords = {fsttcs louisemolitor tobiasfriedrich annamelnichenko pascallenzner year2020}, pages = {15:1&ndash;15:15}, publisher = {Schloss Dagstuhl&ndash;Leibniz-Zentrum f{ü}r Informatik}, title = {Fair Tree Connection Games with Topology-Dependent Edge Cost}, volume = 182, year = 2020 }

Doerr, Benjamin; Krejca, Martin S. Bivariate Estimation-of-Distribution Algorithms Can Find an Exponential Number of OptimaGenetic and Evolutionary Computation Conference (GECCO) 2020: 796–804
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Finding a large set of optima in a multimodal optimization landscape is a challenging task. Classical population-based evolutionary algorithms (EAs) typically converge only to a single solution. While this can be counteracted by applying niching strategies, the number of optima is nonetheless trivially bounded by the population size. Estimation-of-distribution algorithms (EDAs) provide an alternative approach by maintaining a probabilistic model of the solution space instead of an explicit population. Such a model has the benefit of being able to implicitly represent a solution set that is far larger than any realistic population size. To support the study of how optimization algorithms handle large sets of optima, we propose the test function EqualBlocksOneMax (EBOM). It has an easy to optimize fitness landscape, however, with an exponential number of optima. We show that the bivariate EDA mutual-information-maximizing input clustering (MIMIC), without any problem-specific modification, quickly generates a model that behaves very similarly to a theoretically ideal model for that function, which samples each of the exponentially many optima with the same maximal probability.
@inproceedings{doerr2020bivariate, abstract = {Finding a large set of optima in a multimodal optimization landscape is a challenging task. Classical population-based evolutionary algorithms (EAs) typically converge only to a single solution. While this can be counteracted by applying niching strategies, the number of optima is nonetheless trivially bounded by the population size. Estimation-of-distribution algorithms (EDAs) provide an alternative approach by maintaining a probabilistic model of the solution space instead of an explicit population. Such a model has the benefit of being able to implicitly represent a solution set that is far larger than any realistic population size. To support the study of how optimization algorithms handle large sets of optima, we propose the test function EqualBlocksOneMax (EBOM). It has an easy to optimize fitness landscape, however, with an exponential number of optima. We show that the bivariate EDA mutual-information-maximizing input clustering (MIMIC), without any problem-specific modification, quickly generates a model that behaves very similarly to a theoretically ideal model for that function, which samples each of the exponentially many optima with the same maximal probability.}, author = {Doerr, Benjamin and Krejca, Martin S.}, booktitle = {Genetic and Evolutionary Computation Conference (GECCO)}, keywords = {martinskrejca benjamindoerr gecco year2020}, pages = {796–804}, title = {Bivariate Estimation-of-Distribution Algorithms Can Find an Exponential Number of Optima}, year = 2020 }

Bossek, Jakob; Casel, Katrin; Kerschke, Pascal; Neumann, Frank The Node Weight Dependent Traveling Salesperson Problem: Approximation Algorithms and Randomized Search HeuristicsGenetic and Evolutionary Computation Conference (GECCO) 2020: 1286–1294
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Several important optimization problems in the area of vehicle routing can be seen as a variant of the classical Traveling Salesperson Problem (TSP). In the area of evolutionary computation, the traveling thief problem (TTP) has gained increasing interest over the last 5 years. In this paper, we investigate the effect of weights on such problems, in the sense that the cost of traveling increases with respect to the weights of nodes already visited during a tour. This provides abstractions of important TSP variants such as the Traveling Thief Problem and time dependent TSP variants, and allows to study precisely the increase in difficulty caused by weight dependence. We provide a 3.59-approximation for this weight dependent version of TSP with metric distances and bounded positive weights. Furthermore, we conduct experimental investigations for simple randomized local search with classical mutation operators and two variants of the state-of-the-art evolutionary algorithm EAX adapted to the weighted TSP. Our results show the impact of the node weights on the position of the nodes in the resulting tour.
@inproceedings{jakob2020weight, abstract = {Several important optimization problems in the area of vehicle routing can be seen as a variant of the classical Traveling Salesperson Problem (TSP). In the area of evolutionary computation, the traveling thief problem (TTP) has gained increasing interest over the last 5 years. In this paper, we investigate the effect of weights on such problems, in the sense that the cost of traveling increases with respect to the weights of nodes already visited during a tour. This provides abstractions of important TSP variants such as the Traveling Thief Problem and time dependent TSP variants, and allows to study precisely the increase in difficulty caused by weight dependence. We provide a 3.59-approximation for this weight dependent version of TSP with metric distances and bounded positive weights. Furthermore, we conduct experimental investigations for simple randomized local search with classical mutation operators and two variants of the state-of-the-art evolutionary algorithm EAX adapted to the weighted TSP. Our results show the impact of the node weights on the position of the nodes in the resulting tour.}, author = {Bossek, Jakob and Casel, Katrin and Kerschke, Pascal and Neumann, Frank}, booktitle = {Genetic and Evolutionary Computation Conference (GECCO)}, keywords = {sys:relevantfor:ae katrincasel pascalkerschke gecco jakobbossek frankneumann year2020}, pages = {1286-1294}, publisher = {ACM}, title = {The Node Weight Dependent Traveling Salesperson Problem: Approximation Algorithms and Randomized Search Heuristics}, year = 2020 }

Friedrich, Tobias; Krejca, Martin S.; Lagodzinski, J. A. Gregor; Rizzo, Manuel; Zahn, Arthur Memetic Genetic Algorithms for Time Series Compression by Piecewise Linear ApproximationInternational Conference on Neural Information Processing (ICONIP) 2020: 592–604
[ Abstract ] [ BibTeX ] [ DOI ] [ Download ]
 
Time series are sequences of data indexed by time. Such data are collected in various domains, often in massive amounts, such that storing them proves challenging. Thus, time series are commonly stored in a compressed format. An important compression approach is piecewise linear approximation (PLA), which only keeps a small set of time points and interpolates the remainder linearly. Picking a subset of time points such that the PLA minimizes the mean squared error to the original time series is a challenging task, naturally lending itself to heuristics. We propose the piecewise linear approximation genetic algorithm (PLA-GA) for compressing time series by PLA. The PLA-GA is a memetic \((\mu + \lambda)\) GA that makes use of two distinct operators tailored to time series compression. First, we add special individuals to the initial population that are derived using established PLA heuristics. Second, we propose a novel local search operator that greedily improves a compressed time series. We compare the PLA-GA empirically with existing evolutionary approaches and with a deterministic PLA algorithm, known as Bellman's algorithm, that is optimal for the restricted setting of sampling. In both cases, the PLA-GA approximates the original time series better and quicker. Further, it drastically outperforms Bellman's algorithm with increasing instance size with respect to run time until finding a solution of equal or better quality -- we observe speed-up factors between 7 and 100 for instances of 90,000 to 100,000 data points.
@inproceedings{friedrich2020memetic, abstract = {Time series are sequences of data indexed by time. Such data are collected in various domains, often in massive amounts, such that storing them proves challenging. Thus, time series are commonly stored in a compressed format. An important compression approach is piecewise linear approximation (PLA), which only keeps a small set of time points and interpolates the remainder linearly. Picking a subset of time points such that the PLA minimizes the mean squared error to the original time series is a challenging task, naturally lending itself to heuristics. We propose the piecewise linear approximation genetic algorithm (PLA-GA) for compressing time series by PLA. The PLA-GA is a memetic \((\mu + \lambda)\) GA that makes use of two distinct operators tailored to time series compression. First, we add special individuals to the initial population that are derived using established PLA heuristics. Second, we propose a novel local search operator that greedily improves a compressed time series. We compare the PLA-GA empirically with existing evolutionary approaches and with a deterministic PLA algorithm, known as Bellman's algorithm, that is optimal for the restricted setting of sampling. In both cases, the PLA-GA approximates the original time series better and quicker. Further, it drastically outperforms Bellman's algorithm with increasing instance size with respect to run time until finding a solution of equal or better quality &ndash; we observe speed-up factors between 7 and 100 for instances of 90,000 to 100,000 data points.}, author = {Friedrich, Tobias and Krejca, Martin S. and Lagodzinski, J. A. Gregor and Rizzo, Manuel and Zahn, Arthur}, booktitle = {International Conference on Neural Information Processing (ICONIP)}, keywords = {gregorlagodzinski martinskrejca manuelrizzo tobiasfriedrich arthurzahn iconip year2020}, pages = {592-604}, title = {Memetic Genetic Algorithms for Time Series Compression by Piecewise Linear Approximation}, volume = 12534, year = 2020 }

Echzell, Hagen; Friedrich, Tobias; Lenzner, Pascal; Melnichenko, Anna Flow-Based Network Creation GamesInternational Joint Conference on Artificial Intelligence (IJCAI) 2020: 139–145
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Network Creation Games (NCGs) model the creation of decentralized communication networks like the Internet. In such games strategic agents corresponding to network nodes selfishly decide with whom to connect to optimize some objective function. Past research intensively analyzed models where the agents strive for a central position in the network. This models agents optimizing the network for low-latency applications like VoIP. However, with today's abundance of streaming services it is important to ensure that the created network can satisfy the increased bandwidth demand. To the best of our knowledge, this natural problem of the decentralized strategic creation of networks with sufficient bandwidth has not yet been studied. We introduce Flow-Based NCGs where the selfish agents focus on bandwidth instead of latency. In essence, budget-constrained agents create network links to maximize their minimum or average network flow value to all other network nodes. Equivalently, this can also be understood as agents who create links to increase their connectivity and thus also the robustness of the network. For this novel type of NCG we prove that pure Nash equilibria exist, we give a simple algorithm for computing optimal networks, we show that the Price of Stability is~1 and we prove an (almost) tight bound of 2 on the Price of Anarchy. Last but not least, we show that our models do not admit a potential function.
@inproceedings{echzell2020flowbased, abstract = {Network Creation Games (NCGs) model the creation of decentralized communication networks like the Internet. In such games strategic agents corresponding to network nodes selfishly decide with whom to connect to optimize some objective function. Past research intensively analyzed models where the agents strive for a central position in the network. This models agents optimizing the network for low-latency applications like VoIP. However, with today's abundance of streaming services it is important to ensure that the created network can satisfy the increased bandwidth demand. To the best of our knowledge, this natural problem of the decentralized strategic creation of networks with sufficient bandwidth has not yet been studied. We introduce Flow-Based NCGs where the selfish agents focus on bandwidth instead of latency. In essence, budget-constrained agents create network links to maximize their minimum or average network flow value to all other network nodes. Equivalently, this can also be understood as agents who create links to increase their connectivity and thus also the robustness of the network. For this novel type of NCG we prove that pure Nash equilibria exist, we give a simple algorithm for computing optimal networks, we show that the Price of Stability is&nbsp;1 and we prove an (almost) tight bound of 2 on the Price of Anarchy. Last but not least, we show that our models do not admit a potential function.}, author = {Echzell, Hagen and Friedrich, Tobias and Lenzner, Pascal and Melnichenko, Anna}, booktitle = {International Joint Conference on Artificial Intelligence (IJCAI)}, editor = {Bessiere, Christian}, keywords = {ijcai hagenechzell tobiasfriedrich annamelnichenko pascallenzner year2020}, pages = {139-145}, publisher = {ijcai.org}, title = {Flow-Based Network Creation Games}, year = 2020 }

Garg, Naveen; Kumar, Nikhil; Sebö, András Integer Plane Multiflow Maximisation: Flow-Cut Gap and One-Quarter-ApproximationInteger Programming and Combinatorial Optimization (IPCO) 2020: 144–157
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In this paper, we bound the integrality gap and the approximation ratio for maximum plane multiflow problems and deduce bounds on the flow-cut-gap. We consider instances where the union of the supply and demand graphs is planar and prove that there exists a multiflow of value at least half the capacity of a minimum multicut. We then show how to convert any multiflow into a half-integer flow of value at least half the original multiflow. Finally, we round any half-integer multiflow into an integer multiflow, losing at most half the value thus providing a 1/4-approximation algorithm and integrality gap for maximum integer multiflows in the plane.
@inproceedings{garg2020integer, abstract = {In this paper, we bound the integrality gap and the approximation ratio for maximum plane multiflow problems and deduce bounds on the flow-cut-gap. We consider instances where the union of the supply and demand graphs is planar and prove that there exists a multiflow of value at least half the capacity of a minimum multicut. We then show how to convert any multiflow into a half-integer flow of value at least half the original multiflow. Finally, we round any half-integer multiflow into an integer multiflow, losing at most half the value thus providing a 1/4-approximation algorithm and integrality gap for maximum integer multiflows in the plane.}, author = {Garg, Naveen and Kumar, Nikhil and Sebö, András}, booktitle = {Integer Programming and Combinatorial Optimization (IPCO)}, keywords = {ipco nikhilkumar andrassebo naveengarg year2020}, pages = {144-157}, title = {Integer Plane Multiflow Maximisation: Flow-Cut Gap and One-Quarter-Approximation}, volume = 12125, year = 2020 }

Feldmann, Andreas; Issac, Davis; Rai, Ashutosh Fixed-Parameter Tractability of the Weighted Edge Clique Partition ProblemInternational Symposium on Parameterized and Exact Computation (IPEC) 2020: 1–16
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ]
 
We develop an FPT algorithm and a bi-kernel for the Weighted Edge Clique Partition (WECP) problem, where a graph with \(n\) vertices and integer edge weights is given together with an integer \(k\), and the aim is to find \(k\) cliques, such that every edge appears in exactly as many cliques as its weight. The problem has been previously only studied in the unweighted version called Edge Clique Partition (ECP), where the edges need to be partitioned into \(k\) cliques. It was shown that ECP admits a kernel with \(k^2\) vertices [Mujuni and Rosamond, 2008], but this kernel does not extend to WECP. The previously fastest algorithm known for ECP has a runtime of \( 2^O(k^2)}\) \(n^{O(1)}\) [Issac, 2019]. For WECP we develop a bi-kernel with \(4^k\) vertices, and an algorithm with runtime \(2^{O(k^3/2w^1/2\log(k/w)) n^O(1)}\), where \(w\) is the maximum edge weight. The latter in particular improves the runtime for ECP to \(2^{O(k^3/2\log k) n^O(1)}\).
@inproceedings{feldmann2020fixedparameter, abstract = {We develop an FPT algorithm and a bi-kernel for the Weighted Edge Clique Partition (WECP) problem, where a graph with \(n\) vertices and integer edge weights is given together with an integer \(k\), and the aim is to find \(k\) cliques, such that every edge appears in exactly as many cliques as its weight. The problem has been previously only studied in the unweighted version called Edge Clique Partition (ECP), where the edges need to be partitioned into \(k\) cliques. It was shown that ECP admits a kernel with \(k^2\) vertices [Mujuni and Rosamond, 2008], but this kernel does not extend to WECP. The previously fastest algorithm known for ECP has a runtime of \( 2^{O(k^2)}\) \(n^{O(1)}\) [Issac, 2019]. For WECP we develop a bi-kernel with \(4^k\) vertices, and an algorithm with runtime \(2^{O(k^{3/2}w^{1/2}\log(k/w))} n^{O(1)}\), where \(w\) is the maximum edge weight. The latter in particular improves the runtime for ECP to \(2^{O(k^{3/2}\log k)} n^{O(1)}\).}, author = {Feldmann, Andreas and Issac, Davis and Rai, Ashutosh}, booktitle = {International Symposium on Parameterized and Exact Computation (IPEC)}, keywords = {sys:relevantfor:ae ashutoshrai andreasfeldmann ipec davisissac year2020}, pages = {1-16}, title = {Fixed-Parameter Tractability of the Weighted Edge Clique Partition Problem}, year = 2020 }

Kumar, Nikhil Multicommodity Flows in Planar Graphs with Demands on FacesInternational Symposium on Algorithms and Computation (ISAAC) 2020: 1–11
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We consider the problem of multicommodity flows in planar graphs. Seymour showed that if the union of supply and demand graphs is planar, then the cut condition is also sufficient for routing demands. Okamura-Seymour showed that if the supply graph is planar and all demands are incident on one face, then again the cut condition is sufficient for routing demands. We consider a common generalization of these settings where the end points of each demand are on the same face of the planar graph. We show that if the source sink pairs on each face of the graph are such that sources and sinks appear contiguously on the cycle bounding the face, then the flow cut gap is at most 3. We come up with a notion of approximating demands on a face by convex combination of laminar demands to prove this result.
@inproceedings{kumar2020multicommodity, abstract = {We consider the problem of multicommodity flows in planar graphs. Seymour showed that if the union of supply and demand graphs is planar, then the cut condition is also sufficient for routing demands. Okamura-Seymour showed that if the supply graph is planar and all demands are incident on one face, then again the cut condition is sufficient for routing demands. We consider a common generalization of these settings where the end points of each demand are on the same face of the planar graph. We show that if the source sink pairs on each face of the graph are such that sources and sinks appear contiguously on the cycle bounding the face, then the flow cut gap is at most 3. We come up with a notion of approximating demands on a face by convex combination of laminar demands to prove this result.}, author = {Kumar, Nikhil}, booktitle = {International Symposium on Algorithms and Computation (ISAAC)}, keywords = {isaac nikhilkumar year2020}, pages = {1-11}, title = {Multicommodity Flows in Planar Graphs with Demands on Faces}, year = 2020 }

Bilò, Davide; Bilò, Vittorio; Lenzner, Pascal; Molitor, Louise Topological Influence and Locality in Swap Schelling GamesInternational Symposium on Mathematical Foundations of Computer Science (MFCS) 2020: 15:1–15:15
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Residential segregation is a wide-spread phenomenon that can be observed in almost everymajor city. In these urban areas residents with different racial or socioeconomic backgroundtend to form homogeneous clusters. Schelling’s famous agent-based model for residentialsegregation explains how such clusters can form even if all agents are tolerant, i.e., if they agree to live in mixed neighborhoods. For segregation to occur, all it needs is a slightbias towards agents preferring similar neighbors. Very recently, Schelling’s model has beeninvestigated from a game-theoretic point of view with selfish agents that strategically select their residential location. In these games, agents can improve on their current location by performing a location swap with another agent who is willing to swap. We significantly deepen these investigations by studying the influence of the underlying topology modeling the residential area on the existence of equilibria, the Price of Anarchy and on the dynamic properties of the resulting strategic multi-agent system. Moreover, as a new conceptual contribution, we also consider the influence of locality, i.e., if the location swaps are restricted to swaps of neighboring agents. We give improved almost tight boundson the Price of Anarchy for arbitrary underlying graphs and we present (almost) tight bounds for regular graphs, paths and cycles. Moreover, we give almost tight bounds for grids, whichare commonly used in empirical studies. For grids we also show that locality has a severeimpact on the game dynamics.
@inproceedings{bilo2020topological, abstract = {Residential segregation is a wide-spread phenomenon that can be observed in almost everymajor city. In these urban areas residents with different racial or socioeconomic backgroundtend to form homogeneous clusters. Schelling’s famous agent-based model for residentialsegregation explains how such clusters can form even if all agents are tolerant, i.e., if they agree to live in mixed neighborhoods. For segregation to occur, all it needs is a slightbias towards agents preferring similar neighbors. Very recently, Schelling’s model has beeninvestigated from a game-theoretic point of view with selfish agents that strategically select their residential location. In these games, agents can improve on their current location by performing a location swap with another agent who is willing to swap. We significantly deepen these investigations by studying the influence of the underlying topology modeling the residential area on the existence of equilibria, the Price of Anarchy and on the dynamic properties of the resulting strategic multi-agent system. Moreover, as a new conceptual contribution, we also consider the influence of locality, i.e., if the location swaps are restricted to swaps of neighboring agents. We give improved almost tight boundson the Price of Anarchy for arbitrary underlying graphs and we present (almost) tight bounds for regular graphs, paths and cycles. Moreover, we give almost tight bounds for grids, whichare commonly used in empirical studies. For grids we also show that locality has a severeimpact on the game dynamics.}, author = {Bilò, Davide and Bilò, Vittorio and Lenzner, Pascal and Molitor, Louise}, booktitle = {International Symposium on Mathematical Foundations of Computer Science (MFCS)}, editor = {Esparza, Javier and Kr{{á}}l', Daniel}, keywords = {louisemolitor mfcs pascallenzner year2020}, pages = {15:1&ndash;15:15}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum f{{ü}}r Informatik}, series = {LIPIcs}, title = {Topological Influence and Locality in Swap Schelling Games}, volume = 170, year = 2020 }

Michail, Othon; Skretas, George; Spirakis, G. Paul Distributed Computation and Reconfiguration in Actively Dynamic NetworksPrinciples of Distributed Computing (PODC) 2020: 448–457
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In this paper, motivated by recent advances in the algorithmic theory of dynamic networks, we study systems of distributed entities that can actively modify their communication network. This gives rise to distributed algorithms that apart from communication can also exploit network reconfiguration in order to carry out a given task. At the same time, the distributed task itself may now require a global reconfiguration from a given initial network \(G_s\) to a target network \(G_f\) from a family of networks having some good properties, like small diameter. With reasonably powerful computational entities, there is a straightforward algorithm that transforms any \(G_s\) into a spanning clique in \( \mathcal{O (\log n) \) time, where time is measured in synchronous rounds and n is the number of entities. From the clique, the algorithm can then compute any global function on inputs and reconfigure to any desired target network in one additional round. We argue that such a strategy, while time-optimal, is impractical for real applications. In real dynamic networks there is typically a cost associated with creating and maintaining connections. To formally capture such costs, we define three reasonable edge-complexity measures: the total edge activations, the maximum activated edges per round, and the maximum activated degree of a node. The clique formation strategy highlighted above, maximizes all of them. We aim at improved algorithms that will achieve (poly)\(log(n)\) time while minimizing the edge-complexity for the general task of transforming any \(G_s\) into a \(G_f\) of diameter (poly)\(\log(n)\). There is a natural trade-off between time and edge complexity. Our main lower bound shows that \(\Omega(n)\) total edge activations and \(\Omega(n/\log n)\) activations per round must be paid by any algorithm (even centralized) that achieves an optimum of \(\Theta(\log n)\) rounds. On the positive side, we give three distributed algorithms for our general task. The first runs in \(\mathcal{O(log n)\) time, with at most \(2n\) active edges per round, an optimal total of \(\mathcal{O(n \log n)\) edge activations, a maximum degree \(n −1\), and a target network of diameter 2. The second achieves bounded degree by paying an additional logarithmic factor in time and in total edge activations, that is, \(\mathcal{O(\log^2 n)\) and \(\mathcal{O(n \log^2 n)\), respectively. It gives a target network of diameter \(\mathcal{O(\log n)\) and uses \(\mathcal{O(n)\) active edges per round. Our third algorithm shows that if we slightly increase the maximum degree to polylog(n) then we can achieve a running time of \(\mathcal{o(\log^2 n)\). This novel model of distributed computation and reconfiguration in actively dynamic networks and the proposed measures of the edge complexity of distributed algorithms may open new avenues for research in the algorithmic theory of dynamic networks. At the same time, they may serve as an abstraction of more constrained active-reconfiguration systems, such as reconfigurable robotics which come with geometric constraints, and draw interesting connections with alternative network reconfiguration models, like overlay network construction and network constructors. We discuss several open problems and promising future research directions.
@inproceedings{michail2020distributed, abstract = {In this paper, motivated by recent advances in the algorithmic theory of dynamic networks, we study systems of distributed entities that can actively modify their communication network. This gives rise to distributed algorithms that apart from communication can also exploit network reconfiguration in order to carry out a given task. At the same time, the distributed task itself may now require a global reconfiguration from a given initial network \(G_s\) to a target network \(G_f\) from a family of networks having some good properties, like small diameter. With reasonably powerful computational entities, there is a straightforward algorithm that transforms any \(G_s\) into a spanning clique in \( \mathcal{O} (\log n) \) time, where time is measured in synchronous rounds and n is the number of entities. From the clique, the algorithm can then compute any global function on inputs and reconfigure to any desired target network in one additional round. We argue that such a strategy, while time-optimal, is impractical for real applications. In real dynamic networks there is typically a cost associated with creating and maintaining connections. To formally capture such costs, we define three reasonable edge-complexity measures: the total edge activations, the maximum activated edges per round, and the maximum activated degree of a node. The clique formation strategy highlighted above, maximizes all of them. We aim at improved algorithms that will achieve (poly)\(log(n)\) time while minimizing the edge-complexity for the general task of transforming any \(G_s\) into a \(G_f\) of diameter (poly)\(\log(n)\). There is a natural trade-off between time and edge complexity. Our main lower bound shows that \(\Omega(n)\) total edge activations and \(\Omega(n/\log n)\) activations per round must be paid by any algorithm (even centralized) that achieves an optimum of \(\Theta(\log n)\) rounds. On the positive side, we give three distributed algorithms for our general task. The first runs in \(\mathcal{O}(log n)\) time, with at most \(2n\) active edges per round, an optimal total of \(\mathcal{O}(n \log n)\) edge activations, a maximum degree \(n −1\), and a target network of diameter 2. The second achieves bounded degree by paying an additional logarithmic factor in time and in total edge activations, that is, \(\mathcal{O}(\log^2 n)\) and \(\mathcal{O}(n \log^2 n)\), respectively. It gives a target network of diameter \(\mathcal{O}(\log n)\) and uses \(\mathcal{O}(n)\) active edges per round. Our third algorithm shows that if we slightly increase the maximum degree to polylog(n) then we can achieve a running time of \(\mathcal{o}(\log^2 n)\). This novel model of distributed computation and reconfiguration in actively dynamic networks and the proposed measures of the edge complexity of distributed algorithms may open new avenues for research in the algorithmic theory of dynamic networks. At the same time, they may serve as an abstraction of more constrained active-reconfiguration systems, such as reconfigurable robotics which come with geometric constraints, and draw interesting connections with alternative network reconfiguration models, like overlay network construction and network constructors. We discuss several open problems and promising future research directions.}, author = {Michail, Othon and Skretas, George and Spirakis, G. Paul}, booktitle = {Principles of Distributed Computing (PODC)}, keywords = {sys:relevantfor:ae paulgspirakis podc michailothon georgeskretas year2020}, pages = {448&ndash;457}, title = {Distributed Computation and Reconfiguration in Actively Dynamic Networks}, year = 2020 }

Kötzing, Timo; Witt, Carsten Improved Fixed-Budget Results via Drift AnalysisParallel Problem Solving From Nature (PPSN) 2020: 648–660
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Fixed-budget theory is concerned with computing or bounding the fitness value achievable by randomized search heuristics within a given budget of fitness function evaluations. Despite recent progress in fixed-budget theory, there is a lack of general tools to derive such results. We transfer drift theory, the key tool to derive expected optimization times, to the fixed-budged perspective. A first and easy-to-use statement concerned with iterating drift in so-called greed-admitting scenarios immediately translates into bounds on the expected function value. Afterwards, we consider a more general tool based on the well-known variable drift theorem. Applications of this technique to the LeadingOnes benchmark function yield statements that are more precise than the previous state of the art.
@inproceedings{kotzing2020improved, abstract = {Fixed-budget theory is concerned with computing or bounding the fitness value achievable by randomized search heuristics within a given budget of fitness function evaluations. Despite recent progress in fixed-budget theory, there is a lack of general tools to derive such results. We transfer drift theory, the key tool to derive expected optimization times, to the fixed-budged perspective. A first and easy-to-use statement concerned with iterating drift in so-called greed-admitting scenarios immediately translates into bounds on the expected function value. Afterwards, we consider a more general tool based on the well-known variable drift theorem. Applications of this technique to the LeadingOnes benchmark function yield statements that are more precise than the previous state of the art.}, author = {Kötzing, Timo and Witt, Carsten}, booktitle = {Parallel Problem Solving From Nature (PPSN)}, keywords = {sys:relevantfor:ae timokoetzing carstenwitt ppsn year2020}, pages = {648-660}, title = {Improved Fixed-Budget Results via Drift Analysis}, year = 2020 }

Antoniadis, Antonios; Garg, Naveen; Kumar‎, Gunjan; Kumar, Nikhil Parallel Machine Scheduling to Minimize Energy ConsumptionSymposium on Discrete Algorithms (SODA) 2020: 2758–2769
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Given \(n\) jobs with release dates, deadlines and processing times we consider the problem of scheduling them on \(m\) parallel machines so as to minimize the total energy consumed. Machines can enter a sleep state and they consume no energy in this state. Each machine requires \(L\) units of energy to awaken from the sleep state and in its active state the machine can process jobs and consumes a unit of energy per unit time. We allow for preemption and migration of jobs and provide the first constant approximation algorithm for this problem.
@inproceedings{antoniadis2020parallel, abstract = {Given \(n\) jobs with release dates, deadlines and processing times we consider the problem of scheduling them on \(m\) parallel machines so as to minimize the total energy consumed. Machines can enter a sleep state and they consume no energy in this state. Each machine requires \(L\) units of energy to awaken from the sleep state and in its active state the machine can process jobs and consumes a unit of energy per unit time. We allow for preemption and migration of jobs and provide the first constant approximation algorithm for this problem.}, author = {Antoniadis, Antonios and Garg, Naveen and Kumar‎, Gunjan and Kumar, Nikhil}, booktitle = {Symposium on Discrete Algorithms (SODA)}, keywords = {nikhilkumar antoniosantoniadis gunjankumar soda naveengarg year2020}, pages = {2758-2769}, title = {Parallel Machine Scheduling to Minimize Energy Consumption}, year = 2020 }

Feldmann, Michael; Khazraei, Ardalan; Scheideler, Christian Time- and Space-Optimal Clock Synchronization in the Beeping ModelSymposium Parallelism in Algorithms and Architectures (SPAA) 2020: 223–233
[ Abstract ] [ BibTeX ] [ DOI ]
 
We consider the clock synchronization problem in the (discrete) beeping model: Given a network of \(n\) nodes with each node having a clock value \(\delta(v) \in\) \(\{ 0,\ldots , T-1\}\), the goal is to synchronize the clock values of all nodes such that they have the same value in any round. As is standard in clock synchronization, we assume arbitrary activations for all nodes, i.e., the nodes start their protocol at an arbitrary round (not limited to \(\{0,\ldots,T-1\}\)). We give an asymptotically optimal algorithm that runs in \( 4D + \lfloor D/\lfloor T/4 \rfloor \rfloor \cdot\ \)\((T \mod 4) = O(D)\) rounds, where \(D\) is the diameter of the network. Once all nodes are in sync, they beep at the same round every \(T\) rounds. The algorithm drastically improves on the \(O(T D)\)-bound of [Alistarh et al. 2013] (where \(T\) is required to be at least \(4n\), so the bound is no better than \(O(nD)\)). Our algorithm is very simple as nodes only have to maintain \(3\) bits in addition to the \(\lceil \log T \rceil\) bits needed to maintain the clock. Furthermore we investigate the complexity of self-stabilizing solutions for the clock synchronization problem: We first show lower bounds of \(\Omega(\max\{T,n\})\) rounds on the runtime and \(\Omega(\log(\max\{T,n\}))\) bits of memory required for any such protocol. Afterwards we present a protocol that runs in \(O(\max\{T,n\})\) rounds using at most \(O(\log(\max\{T,n\}))\) bits at each node, which is asymptotically optimal with regards to both, runtime and memory requirements.
@inproceedings{feldmann2020spaceoptimal, abstract = {We consider the clock synchronization problem in the (discrete) beeping model: Given a network of \(n\) nodes with each node having a clock value \(\delta(v) \in\) \(\{ 0,\ldots , T-1\}\), the goal is to synchronize the clock values of all nodes such that they have the same value in any round. As is standard in clock synchronization, we assume arbitrary activations for all nodes, i.e., the nodes start their protocol at an arbitrary round (not limited to \(\{0,\ldots,T-1\}\)). We give an asymptotically optimal algorithm that runs in \( 4D + \lfloor D/\lfloor T/4 \rfloor \rfloor \cdot\ \)\((T \mod 4) = O(D)\) rounds, where \(D\) is the diameter of the network. Once all nodes are in sync, they beep at the same round every \(T\) rounds. The algorithm drastically improves on the \(O(T D)\)-bound of [Alistarh et al. 2013] (where \(T\) is required to be at least \(4n\), so the bound is no better than \(O(nD)\)). Our algorithm is very simple as nodes only have to maintain \(3\) bits in addition to the \(\lceil \log T \rceil\) bits needed to maintain the clock. Furthermore we investigate the complexity of self-stabilizing solutions for the clock synchronization problem: We first show lower bounds of \(\Omega(\max\{T,n\})\) rounds on the runtime and \(\Omega(\log(\max\{T,n\}))\) bits of memory required for any such protocol. Afterwards we present a protocol that runs in \(O(\max\{T,n\})\) rounds using at most \(O(\log(\max\{T,n\}))\) bits at each node, which is asymptotically optimal with regards to both, runtime and memory requirements.}, author = {Feldmann, Michael and Khazraei, Ardalan and Scheideler, Christian}, booktitle = {Symposium Parallelism in Algorithms and Architectures (SPAA)}, keywords = {christianscheideler sys:relevantfor:ae michaelfeldmann ardalankhazraei spaa year2020}, pages = {223-233}, title = {Time- and Space-Optimal Clock Synchronization in the Beeping Model}, year = 2020 }

Bläsius, Thomas; Fischbeck, Philipp; Friedrich, Tobias; Katzmann, Maximilian Solving Vertex Cover in Polynomial Time on Hyperbolic Random GraphsSymposium on the Theoretical Aspects of Computer Science (STACS) 2020: 25:1–25:14
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
The VertexCover problem is proven to be computationally hard in different ways: It is NP-complete to find an optimal solution and even NP-hard to find an approximation with reasonable factors. In contrast, recent experiments suggest that on many real-world networks the run time to solve VertexCover is way smaller than even the best known FPT-approaches can explain. Similarly, greedy algorithms deliver very good approximations to the optimal solution in practice. We link these observations to two properties that are observed in many real-world networks, namely a heterogeneous degree distribution and high clustering. To formalize these properties and explain the observed behavior, we analyze how a branch-and-reduce algorithm performs on hyperbolic random graphs, which have become increasingly popular for modeling real-world networks. In fact, we are able to show that the VertexCover problem on hyperbolic random graphs can be solved in polynomial time, with high probability. The proof relies on interesting structural properties of hyperbolic random graphs. Since these predictions of the model are interesting in their own right, we conducted experiments on real-world networks showing that these properties are also observed in practice. When utilizing the same structural properties in an adaptive greedy algorithm, further experiments suggest that, on real instances, this leads to better approximations than the standard greedy approach within reasonable time. We link these observations to two properties that are observed in many real-world networks, namely a heterogeneous degree distribution and high clustering. To formalize these properties and explain the observed behavior, we analyze how a branch-and-reduce algorithm performs on hyperbolic random graphs, which have become increasingly popular for modeling real-world networks. In fact, we are able to show that the VertexCover problem on hyperbolic random graphs can be solved in polynomial time, with high probability. The proof relies on interesting structural properties of hyperbolic random graphs. Since these predictions of the model are interesting in their own right, we conducted experiments on real-world networks showing that these properties are also observed in practice. When utilizing the same structural properties in an adaptive greedy algorithm, further experiments suggest that this leads to even better approximations than the standard greedy approach on real instances.
@inproceedings{blasius2020solving, abstract = {The VertexCover problem is proven to be computationally hard in different ways: It is NP-complete to find an optimal solution and even NP-hard to find an approximation with reasonable factors. In contrast, recent experiments suggest that on many real-world networks the run time to solve VertexCover is way smaller than even the best known FPT-approaches can explain. Similarly, greedy algorithms deliver very good approximations to the optimal solution in practice. We link these observations to two properties that are observed in many real-world networks, namely a heterogeneous degree distribution and high clustering. To formalize these properties and explain the observed behavior, we analyze how a branch-and-reduce algorithm performs on hyperbolic random graphs, which have become increasingly popular for modeling real-world networks. In fact, we are able to show that the VertexCover problem on hyperbolic random graphs can be solved in polynomial time, with high probability. The proof relies on interesting structural properties of hyperbolic random graphs. Since these predictions of the model are interesting in their own right, we conducted experiments on real-world networks showing that these properties are also observed in practice. When utilizing the same structural properties in an adaptive greedy algorithm, further experiments suggest that, on real instances, this leads to better approximations than the standard greedy approach within reasonable time. We link these observations to two properties that are observed in many real-world networks, namely a heterogeneous degree distribution and high clustering. To formalize these properties and explain the observed behavior, we analyze how a branch-and-reduce algorithm performs on hyperbolic random graphs, which have become increasingly popular for modeling real-world networks. In fact, we are able to show that the VertexCover problem on hyperbolic random graphs can be solved in polynomial time, with high probability. The proof relies on interesting structural properties of hyperbolic random graphs. Since these predictions of the model are interesting in their own right, we conducted experiments on real-world networks showing that these properties are also observed in practice. When utilizing the same structural properties in an adaptive greedy algorithm, further experiments suggest that this leads to even better approximations than the standard greedy approach on real instances.}, author = {Bläsius, Thomas and Fischbeck, Philipp and Friedrich, Tobias and Katzmann, Maximilian}, booktitle = {Symposium on the Theoretical Aspects of Computer Science (STACS)}, keywords = {philippfischbeck thomasblaesius stacs tobiasfriedrich maximiliankatzmann hyperbolic_analysis year2020}, pages = {25:1-25:14}, title = {Solving Vertex Cover in Polynomial Time on Hyperbolic Random Graphs}, year = 2020 }

Chechik, Shiri; Cohen, Sarel Distance sensitivity oracles with subcubic preprocessing time and fast query timeSymposium Theory of Computing (STOC) 2020: 1375–1388
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We present the first distance sensitivity oracle (DSO) with subcubic preprocessing time and poly-logarithmic query time for directed graphs with integer weights in the range \([−M,M]\). Weimann and Yuster [FOCS 10] presented a distance sensitivity oracle for a single vertex/edge failure with subcubic preprocessing time of \(\mathcal{O(Mn^\omega+1− \alpha})\) and subquadratic query time of \(\tilde{\mathcal{O(n^{1+\alpha})\), where \(\alpha\) is any parameter in \([0,1]\), \(n\) is the number of vertices, \(m\) is the number of edges, the \(\tilde{\mathcal{O(·)\) notation hides poly-logarithmic factors in \(n\) and \(\omega<2.373\) is the matrix multiplication exponent.Later, Grandoni and Vassilevska Williams [FOCS 12] substantially improved the query time to sublinear in \(n\). In particular, they presented a distance sensitivity oracle for a single vertex/edge failure with \(\tilde{\mathcal{O}}\)\( (Mn^\omega +1/2}\) \(+ Mn^\omega+\alpha(4−\omega)})\) preprocessing time and \(\tilde{\mathcal{O(n^{1−\alpha})\) query time. Despite the substantial improvement in the query time, it still remains polynomial in the size of the graph, which may be undesirable in many settings where the graph is of large scale. A natural question is whether one can hope for a distance sensitivity oracle with subcubic preprocessing time and very fast query time (of poly-logarithmic in \(n\)). In this paper we answer this question affirmatively by presenting a distance sensitive oracle supporting a single vertex/edge failure in subcubic \(\tilde{\mathcal{O(Mn^{2.873})\) preprocessing time for \(\omega=2.373\), \(\tilde{\mathcal{O(n^{2.5})\) space and near optimal query time of \(\tilde{\mathcal{O(1)\). For comparison, with the same \(\tilde{\mathcal{O(Mn^{2.873})\) preprocessing time the DSO of Grandoni and Vassilevska Williams has \(\tilde{\mathcal{O(n^{0.693})\) query time. In fact, the best query time their algorithm can obtain is \(\tilde{\mathcal{O(Mn^{0.385})\) (with \(\tilde{\mathcal{O(Mn^3)\) preprocessing time).
@inproceedings{chechik2020distance, abstract = {We present the first distance sensitivity oracle (DSO) with subcubic preprocessing time and poly-logarithmic query time for directed graphs with integer weights in the range \([−M,M]\). Weimann and Yuster [FOCS 10] presented a distance sensitivity oracle for a single vertex/edge failure with subcubic preprocessing time of \(\mathcal{O}(Mn^{\omega+1− \alpha})\) and subquadratic query time of \(\tilde{\mathcal{O}}(n^{1+\alpha})\), where \(\alpha\) is any parameter in \([0,1]\), \(n\) is the number of vertices, \(m\) is the number of edges, the \(\tilde{\mathcal{O}}(·)\) notation hides poly-logarithmic factors in \(n\) and \(\omega<2.373\) is the matrix multiplication exponent.Later, Grandoni and Vassilevska Williams [FOCS 12] substantially improved the query time to sublinear in \(n\). In particular, they presented a distance sensitivity oracle for a single vertex/edge failure with \(\tilde{\mathcal{O}}\)\( (Mn^{\omega +1/2}\) \(+ Mn^{\omega+\alpha(4−\omega)})\) preprocessing time and \(\tilde{\mathcal{O}}(n^{1−\alpha})\) query time. Despite the substantial improvement in the query time, it still remains polynomial in the size of the graph, which may be undesirable in many settings where the graph is of large scale. A natural question is whether one can hope for a distance sensitivity oracle with subcubic preprocessing time and very fast query time (of poly-logarithmic in \(n\)). In this paper we answer this question affirmatively by presenting a distance sensitive oracle supporting a single vertex/edge failure in subcubic \(\tilde{\mathcal{O}}(Mn^{2.873})\) preprocessing time for \(\omega=2.373\), \(\tilde{\mathcal{O}}(n^{2.5})\) space and near optimal query time of \(\tilde{\mathcal{O}}(1)\). For comparison, with the same \(\tilde{\mathcal{O}}(Mn^{2.873})\) preprocessing time the DSO of Grandoni and Vassilevska Williams has \(\tilde{\mathcal{O}}(n^{0.693})\) query time. In fact, the best query time their algorithm can obtain is \(\tilde{\mathcal{O}}(Mn^{0.385})\) (with \(\tilde{\mathcal{O}}(Mn^3)\) preprocessing time).}, author = {Chechik, Shiri and Cohen, Sarel}, booktitle = {Symposium Theory of Computing (STOC)}, keywords = {sarelcohen sys:relevantfor:ae stoc shirichechik year2020}, pages = {1375-1388}, title = {Distance sensitivity oracles with subcubic preprocessing time and fast query time}, year = 2020 }

Becher, Kilian; Lagodzinski, J. A. Gregor; Strufe, Thorsten Privacy-Preserving Public Verification of Ethical Cobalt SourcingTrust, Security and Privacy in Computing and Communications (TrustCom) 2020: 998–1005
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Cobalt is a key ingredient of lithium-ion batteries and therefore is crucial for many modern devices. To ensure ethical sourcing, consumers need a way to verify provenance of their cobalt-based products, including the percentage of artisanally mined (ASM) cobalt. Existing frameworks for provenance and supply chain traceability rely on distributed ledgers. Providing public verifiability via permissionless distributed ledgers is trivial. However, offering public verifiability based on confidential production details seems contradictory. Hence, existing frameworks lack public verifiability of ratios between commodities while ensuring confidentiality of supply chain details. We propose a protocol that allows end consumers to verify the percentage of ASM cobalt in their products. Unlike previous solutions, production details are published and processed entirely in encrypted form by employing homomorphic encryption and proxy re-encryption. Thus, it ensures a high level of confidentiality of supply chain data. It has constant consumer-side complexity, making it suitable for mobile devices.