All Publications

2024

Bläsius, Thomas; Fischbeck, Philipp On the External Validity of Average-Case Analyses of Graph AlgorithmsACM Transactions on Algorithms 2024
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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 2740 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.
@article{blasius2023external, 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 2740 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}, journal = {ACM Transactions on Algorithms}, keywords = {talg philippfischbeck thomasblaesius year2024}, number = 1, publisher = {Association for Computing Machinery}, title = {On the External Validity of Average-Case Analyses of Graph Algorithms}, volume = 20, year = 2024 }

Casel, Katrin; Friedrich, Tobias; Neubert, Stefan; Schmid, Markus L. Shortest distances as enumeration problemDiscrete Applied Mathematics 2024: 89–103
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We investigate the single source shortest distance (SSSD) and all pairs shortest distance (APSD) problems as enumeration problems (on unweighted and integer weighted graphs), meaning that the elements (u,v,d(u,v)) – where u and v are vertices with shortest distance d(u,v) – are produced and listed one by one without repetition. The performance is measured in the RAM model of computation with respect to preprocessing time and delay, i.e., the maximum time that elapses between two consecutive outputs. This point of view reveals that specific types of output (e.g., excluding the non-reachable pairs (u,v,∞), or excluding the self-distances (u,u,0)) and the order of enumeration (e.g., sorted by distance, sorted row-wise with respect to the distance matrix) have a huge impact on the complexity of APSD while they appear to have no effect on SSSD. In particular, we show for APSD that enumeration without output restrictions is possible with delay in the order of the average degree. Excluding non-reachable pairs, or requesting the output to be sorted by distance, increases this delay to the order of the maximum degree. Further, for weighted graphs, a delay in the order of the average degree is also not possible without preprocessing or considering self-distances as output. In contrast, for SSSD we find that a delay in the order of the maximum degree without preprocessing is attainable and unavoidable for any of these requirements.
@article{casel2024shortest, abstract = {We investigate the single source shortest distance (SSSD) and all pairs shortest distance (APSD) problems as enumeration problems (on unweighted and integer weighted graphs), meaning that the elements (u,v,d(u,v)) – where u and v are vertices with shortest distance d(u,v) – are produced and listed one by one without repetition. The performance is measured in the RAM model of computation with respect to preprocessing time and delay, i.e., the maximum time that elapses between two consecutive outputs. This point of view reveals that specific types of output (e.g., excluding the non-reachable pairs (u,v,∞), or excluding the self-distances (u,u,0)) and the order of enumeration (e.g., sorted by distance, sorted row-wise with respect to the distance matrix) have a huge impact on the complexity of APSD while they appear to have no effect on SSSD. In particular, we show for APSD that enumeration without output restrictions is possible with delay in the order of the average degree. Excluding non-reachable pairs, or requesting the output to be sorted by distance, increases this delay to the order of the maximum degree. Further, for weighted graphs, a delay in the order of the average degree is also not possible without preprocessing or considering self-distances as output. In contrast, for SSSD we find that a delay in the order of the maximum degree without preprocessing is attainable and unavoidable for any of these requirements.}, author = {Casel, Katrin and Friedrich, Tobias and Neubert, Stefan and Schmid, Markus L.}, journal = {Discrete Applied Mathematics}, keywords = {sys:relevantfor:ae katrincasel tobiasfriedrich year2024 dam stefanneubert}, month = 1, pages = {89-103}, title = {Shortest distances as enumeration problem}, volume = 342, year = 2024 }

Berenbrink, Petra; Hoefer, Martin; Kaaser, Dominik; Lenzner, Pascal; Rau, Malin; Schmand, Daniel Asynchronous Opinion Dynamics in Social NetworksDistributed Computing 2024
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Opinion spreading in a society decides the fate of elections, the success of products, and the impact of political or social movements. A prominent model to study opinion formation processes is due to Hegselmann and Krause. It has the distinguishing feature that stable states do not necessarily show consensus, i.e., the population of agents might not agree on the same opinion. We focus on the social variant of the Hegselmann-Krause model. There are \(n\) agents, which are connected by a social network. Their opinions evolve in an iterative, asynchronous process, in which agents are activated one after another at random. When activated, an agent adopts the average of the opinions of its neighbors having a similar opinion (where similarity of opinions is defined using a parameter \(\varepsilon\)). Thus, the set of influencing neighbors of an agent may change over time. We show that such opinion dynamics are guaranteed to converge for any social network. We provide an upper bound of \(O(nE^2 (\varepsilon/\delta)^2)\) on the expected number of opinion updates until convergence to a stable state, where \(E\rvert\) is the number of edges of the social network, and \($\delta$\) is a parameter of the stability concept. For the complete social network we show a bound of \(O(n^3(n^2 + (\varepsilon/\delta)^2))\) that represents a major improvement over the previously best upper bound of \(O(n^9 (\varepsilon/\delta)^2)\).
@article{berenbrink2024asynchronous, abstract = {Opinion spreading in a society decides the fate of elections, the success of products, and the impact of political or social movements. A prominent model to study opinion formation processes is due to Hegselmann and Krause. It has the distinguishing feature that stable states do not necessarily show consensus, i.e., the population of agents might not agree on the same opinion. We focus on the social variant of the Hegselmann-Krause model. There are \(n\) agents, which are connected by a social network. Their opinions evolve in an iterative, asynchronous process, in which agents are activated one after another at random. When activated, an agent adopts the average of the opinions of its neighbors having a similar opinion (where similarity of opinions is defined using a parameter \(\varepsilon\)). Thus, the set of influencing neighbors of an agent may change over time. We show that such opinion dynamics are guaranteed to converge for any social network. We provide an upper bound of \(O(nE^2 (\varepsilon/\delta)^2)\) on the expected number of opinion updates until convergence to a stable state, where \(E\rvert\) is the number of edges of the social network, and $\delta$ is a parameter of the stability concept. For the complete social network we show a bound of \(O(n^3(n^2 + (\varepsilon/\delta)^2))\) that represents a major improvement over the previously best upper bound of \(O(n^9 (\varepsilon/\delta)^2)\).}, author = {Berenbrink, Petra and Hoefer, Martin and Kaaser, Dominik and Lenzner, Pascal and Rau, Malin and Schmand, Daniel}, journal = {Distributed Computing}, keywords = {year2024 pascallenzner}, title = {Asynchronous Opinion Dynamics in Social Networks}, year = 2024 }

Friedrich, Tobias; Göbel, Andres; Klodt, Nicolas; Krejca, Martin S.; Pappik, Marcus Analysis of the survival time of the SIRS process via expansionElectronic Journal of Probability 2024: 1–29
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We study the SIRS process---a continuous-time Markov chain modeling the spread of infections on graphs. In this model, vertices are either susceptible, infected, or recovered. Each infected vertex becomes recovered at rate 1 and infects each of its susceptible neighbors independently at rate~\(\lambda\), and each recovered vertex becomes susceptible at a rate~\(\varrho\), which we assume to be independent of the graph size. A central quantity of the SIRS process is the time until no vertex is infected, known as the survival time. Surprisingly though, to the best of our knowledge, all known rigorous theoretical results that exist so far immediately carry over from the related SIS model and do not completely explain the behavior of the SIRS process. We address this imbalance by conducting theoretical analyses of the SIRS process via the expansion properties of the underlying graph. Our first result shows that the expected survival time of the SIRS process on stars is at most polynomial in the graph size for any value of~\(\lambda\). This behavior is fundamentally different from the SIS process, where the expected survival time is exponential already for small infection rates. This raises the question of which graph properties result in an exponential survival time. Our main result is an exponential lower bound of the expected survival time of the SIRS process on expander graphs. Specifically, we show that on expander graphs \(G\) with \(n\) vertices, degree close to \(d\), and sufficiently small spectral expansion, the SIRS process has expected survival time at least exponential in \(n\) when \(\lambda \geq c/d\) for a constant \(c > 1\). Previous results on the SIS process show that this bound is almost tight. Additionally, our result holds even if \(G\) is a subgraph. Notably, our result implies an almost-tight threshold for Erdos-Renyi-graphs and a regime of exponential survival time for complex network models. The proof of our main result draws inspiration from Lyapunov functions used in mean-field theory to devise a two-dimensional potential function and from applying a negative-drift theorem to show that the expected survival time is exponential.
@article{friedrich2024analysis, abstract = {We study the SIRS process—a continuous-time Markov chain modeling the spread of infections on graphs. In this model, vertices are either susceptible, infected, or recovered. Each infected vertex becomes recovered at rate 1 and infects each of its susceptible neighbors independently at rate \(\lambda\), and each recovered vertex becomes susceptible at a rate \(\varrho\), which we assume to be independent of the graph size. A central quantity of the SIRS process is the time until no vertex is infected, known as the survival time. Surprisingly though, to the best of our knowledge, all known rigorous theoretical results that exist so far immediately carry over from the related SIS model and do not completely explain the behavior of the SIRS process. We address this imbalance by conducting theoretical analyses of the SIRS process via the expansion properties of the underlying graph. Our first result shows that the expected survival time of the SIRS process on stars is at most polynomial in the graph size for any value of \(\lambda\). This behavior is fundamentally different from the SIS process, where the expected survival time is exponential already for small infection rates. This raises the question of which graph properties result in an exponential survival time. Our main result is an exponential lower bound of the expected survival time of the SIRS process on expander graphs. Specifically, we show that on expander graphs \(G\) with \(n\) vertices, degree close to \(d\), and sufficiently small spectral expansion, the SIRS process has expected survival time at least exponential in \(n\) when \(\lambda \geq c/d\) for a constant \(c > 1\). Previous results on the SIS process show that this bound is almost tight. Additionally, our result holds even if \(G\) is a subgraph. Notably, our result implies an almost-tight threshold for Erdos-Renyi-graphs and a regime of exponential survival time for complex network models. The proof of our main result draws inspiration from Lyapunov functions used in mean-field theory to devise a two-dimensional potential function and from applying a negative-drift theorem to show that the expected survival time is exponential.}, author = {Friedrich, Tobias and Göbel, Andres and Klodt, Nicolas and Krejca, Martin S. and Pappik, Marcus}, journal = {Electronic Journal of Probability}, keywords = {nicolasklodt marcuspappik martinskrejca andreasgoebel tobiasfriedrich ejp year2024}, pages = {1-29}, title = {Analysis of the survival time of the SIRS process via expansion}, volume = 29, year = 2024 }

Sauer, Pascal; Cseh, Ágnes; Lenzner, Pascal Improving ranking quality and fairness in Swiss-system chess tournamentsJournal of Quantitative Analysis in Sports 2024
[ BibTeX ]
 
@article{sauer2024improving, author = {Sauer, Pascal and Cseh, Ágnes and Lenzner, Pascal}, journal = {Journal of Quantitative Analysis in Sports}, keywords = {year2024 pascallenzner}, title = {Improving ranking quality and fairness in Swiss-system chess tournaments}, year = 2024 }

Bilò, Davide; Friedrich, Tobias; Lenzner, Pascal; Melnichenko, Anna Geometric Network Creation GamesSIAM Journal on Discrete Mathematics 2024: 277–315
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Network creation games are a well-known approach for explaining and analyzing the structure, quality, and dynamics of real-world networks that evolved via the interaction of selfish agents without a central authority. In these games selfish agents corresponding to nodes in a network strategically buy incident edges to improve their centrality. However, past research on these games only considered the creation of networks with unit-weight edges. In practice, e.g., when constructing a fiber-optic network, the choice of which nodes to connect and also the induced price for a link crucially depend on the distance between the involved nodes, and such settings can be modeled via edge-weighted graphs. We incorporate arbitrary edge weights by generalizing the well-known model by Fabrikant et al. [Proceedings of PODC ’03, ACM, 2003, pp. 347–351] to edge-weighted host graphs and focus on the geometric setting where the weights are induced by the distances in some metric space. In stark contrast to the state of the art for the unit-weight version, where the price of anarchy is conjectured to be constant and where resolving this is a major open problem, we prove a tight nonconstant bound on the price of anarchy for the metric version and a slightly weaker upper bound for the nonmetric case. Moreover, we analyze the existence of equilibria, the computational hardness, and the game dynamics for several natural metrics. The model we propose can be seen as the game-theoretic analogue of the classical network design problem. Thus, low-cost equilibria of our game correspond to decentralized and stable approximations of the optimum network design.
@article{bilo2023geometric, abstract = {Network creation games are a well-known approach for explaining and analyzing the structure, quality, and dynamics of real-world networks that evolved via the interaction of selfish agents without a central authority. In these games selfish agents corresponding to nodes in a network strategically buy incident edges to improve their centrality. However, past research on these games only considered the creation of networks with unit-weight edges. In practice, e.g., when constructing a fiber-optic network, the choice of which nodes to connect and also the induced price for a link crucially depend on the distance between the involved nodes, and such settings can be modeled via edge-weighted graphs. We incorporate arbitrary edge weights by generalizing the well-known model by Fabrikant et al. [Proceedings of PODC ’03, ACM, 2003, pp. 347–351] to edge-weighted host graphs and focus on the geometric setting where the weights are induced by the distances in some metric space. In stark contrast to the state of the art for the unit-weight version, where the price of anarchy is conjectured to be constant and where resolving this is a major open problem, we prove a tight nonconstant bound on the price of anarchy for the metric version and a slightly weaker upper bound for the nonmetric case. Moreover, we analyze the existence of equilibria, the computational hardness, and the game dynamics for several natural metrics. The model we propose can be seen as the game-theoretic analogue of the classical network design problem. Thus, low-cost equilibria of our game correspond to decentralized and stable approximations of the optimum network design.}, author = {Bilò, Davide and Friedrich, Tobias and Lenzner, Pascal and Melnichenko, Anna}, journal = {SIAM Journal on Discrete Mathematics}, keywords = {sidma tobiasfriedrich year2024 annamelnichenko pascallenzner}, number = 1, pages = {277-315}, title = {Geometric Network Creation Games}, volume = 38, year = 2024 }

Friedrich, Tobias; Göbel, Andreas; Katzmann, Maximilian; Schiller, Leon Cliques in High-Dimensional Geometric Inhomogeneous Random GraphsSIAM Journal on Discrete Mathematics 2024: 1943–2000
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A recent trend in the context of graph theory is to bring theoretical analyses closer to empirical observations, by focusing the studies on random graph models that are used to represent practical instances. There, it was observed that geometric inhomogeneous random graphs (GIRGs) yield good representations of complex real-world networks, by expressing edge probabilities as a function that depends on (heterogeneous) vertex weights and distances in some underlying geometric space that the vertices are distributed in. While most of the parameters of the model are understood well, it was unclear how the dimensionality of the ground space affects the structure of the graphs. In this paper, we complement existing research into the dimension of geometric random graph models and the ongoing study of determining the dimensionality of real-world networks, by studying how the structure of GIRGs changes as the number of dimensions increases. We prove that, in the limit, GIRGs approach non-geometric inhomogeneous random graphs and present insights on how quickly the decay of the geometry impacts important graph structures. In particular, we study the expected number of cliques of a given size as well as the clique number and characterize phase transitions at which their behavior changes fundamentally. Finally, our insights help in better understanding previous results about the impact of the dimensionality on geometric random graphs.
@article{friedrich2024cliques, abstract = {A recent trend in the context of graph theory is to bring theoretical analyses closer to empirical observations, by focusing the studies on random graph models that are used to represent practical instances. There, it was observed that geometric inhomogeneous random graphs (GIRGs) yield good representations of complex real-world networks, by expressing edge probabilities as a function that depends on (heterogeneous) vertex weights and distances in some underlying geometric space that the vertices are distributed in. While most of the parameters of the model are understood well, it was unclear how the dimensionality of the ground space affects the structure of the graphs. In this paper, we complement existing research into the dimension of geometric random graph models and the ongoing study of determining the dimensionality of real-world networks, by studying how the structure of GIRGs changes as the number of dimensions increases. We prove that, in the limit, GIRGs approach non-geometric inhomogeneous random graphs and present insights on how quickly the decay of the geometry impacts important graph structures. In particular, we study the expected number of cliques of a given size as well as the clique number and characterize phase transitions at which their behavior changes fundamentally. Finally, our insights help in better understanding previous results about the impact of the dimensionality on geometric random graphs.}, author = {Friedrich, Tobias and Göbel, Andreas and Katzmann, Maximilian and Schiller, Leon}, journal = {SIAM Journal on Discrete Mathematics}, keywords = {SIMDA andreasgoebel tobiasfriedrich year2024}, number = 2, pages = {1943-2000}, title = {Cliques in High-Dimensional Geometric Inhomogeneous Random Graphs}, volume = 38, year = 2024 }

Jana, Satyabrata; Saha, Souvik; Sahu, Abhishek; Saurabh, Saket; Verma, Shaily Partitioning subclasses of chordal graphs with few deletionsTheoretical Computer Science 2024: 114288
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In the (Vertex) \(k\)-Way Cut problem, input is an undirected graph \(G\), an integer \(s\), and the goal is to find a subset \(S\) of edges (vertices) of size at most \(s\), such that \(G-S\) has at least \(k\) connected components. Downey et al. [Electr. Notes Theor. Comput. Sci. 2003] showed that \(k\)-Way Cut is W[1]-hard parameterized by \( k \). However, Kawarabayashi and Throup [FOCS 2011] showed that the problem is fixed-parameter tractable (FPT) in general graphs with respect to the parameter \(s\) and provided a \( \mathcal{O(s^s^\mathcal{O(s) n^2) \) time algorithm, where \(n \) denotes the number of vertices in \(G \). The best-known algorithm for this problem runs in time \(s^{\mathcal{O(s) n^\mathcal{O(1)}\) given by Lokshtanov et al. [ACM Tran. of Algo. 2021]. On the other hand, Vertex \(k\)-Way Cut is W[1]-hard with respect to either of the parameters, \(k\) or \(s\) or \(k+s\). These algorithmic results motivate us to look at the problems on special classes of graphs. In this paper, we consider the (Vertex) \(k\)-Way Cut problem on subclasses of chordal graphs and obtain the following results. We first give a sub-exponential FPT algorithm for \(k\)-Way Cut running in time \(2^{\mathcal{O(\sqrt{s} \log s) n^\mathcal{O(1)}\) on chordal graphs. It is known that Vertex \(k\)-Way Cut is W[1]-hard on chordal graphs, in fact on split graphs, parameterized by \(k+s\). We complement this hardness result by designing polynomial-time algorithms for Vertex \(k\)-Way Cut on interval graphs, circular-arc graphs and permutation graphs.
@article{DBLP:journals/tcs/JanaSSSV24, abstract = {In the (Vertex) \(k\)-Way Cut problem, input is an undirected graph \(G\), an integer \(s\), and the goal is to find a subset \(S\) of edges (vertices) of size at most \(s\), such that \(G-S\) has at least \(k\) connected components. Downey et al. [Electr. Notes Theor. Comput. Sci. 2003] showed that \(k\)-Way Cut is W[1]-hard parameterized by \( k \). However, Kawarabayashi and Throup [FOCS 2011] showed that the problem is fixed-parameter tractable (FPT) in general graphs with respect to the parameter \(s\) and provided a \( \mathcal{O}(s^{s^{\mathcal{O}(s)}} n^2) \) time algorithm, where \(n \) denotes the number of vertices in \(G \). The best-known algorithm for this problem runs in time \(s^{\mathcal{O}(s)} n^{\mathcal{O}(1)}\) given by Lokshtanov et al. [ACM Tran. of Algo. 2021]. On the other hand, Vertex \(k\)-Way Cut is W[1]-hard with respect to either of the parameters, \(k\) or \(s\) or \(k+s\). These algorithmic results motivate us to look at the problems on special classes of graphs. In this paper, we consider the (Vertex) \(k\)-Way Cut problem on subclasses of chordal graphs and obtain the following results. We first give a sub-exponential FPT algorithm for \(k\)-Way Cut running in time \(2^{\mathcal{O}(\sqrt{s} \log s)} n^{\mathcal{O}(1)}\) on chordal graphs. It is known that Vertex \(k\)-Way Cut is W[1]-hard on chordal graphs, in fact on split graphs, parameterized by \(k+s\). We complement this hardness result by designing polynomial-time algorithms for Vertex \(k\)-Way Cut on interval graphs, circular-arc graphs and permutation graphs.}, author = {Jana, Satyabrata and Saha, Souvik and Sahu, Abhishek and Saurabh, Saket and Verma, Shaily}, journal = {Theoretical Computer Science}, keywords = {tcs shailyverma year2024}, pages = 114288, title = {Partitioning subclasses of chordal graphs with few deletions}, year = 2024 }

Bilò, Davide; Chechik, Shiri; Choudhary, Keerti; Cohen, Sarel; Friedrich, Tobias; Krogmann, Simon; Schirneck, Martin Approximate Distance Sensitivity Oracles in Subquadratic SpaceTheoretiCS 2024
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An \(f\)-edge fault-tolerant distance sensitive oracle (\(f\)-DSO) with stretch \(\sigma\ge{}1\) is a data structure that preprocesses a given undirected, unweighted graph \(G\) with \(n\) vertices and \(m\) edges, and a positive integer \(f\). When queried with a pair of vertices \(s,t\) and a set \(F\) of at most \(f\) edges, it returns a \(\sigma\)-approximation of the \(s\)-\(t\)-distance in \(G-F\). We study \(f\)-DSOs that take subquadratic space. Thorup and Zwick [JACM~2005] showed that this is only possible for \(\sigma \ge 3\). We present, for any constant \(f\ge{}1\) and \(\alpha\in(0,\frac{1}{2})\), and any \(\varepsilon>0\), a randomized \(f\)-DSO with stretch \( 3+\varepsilon\) that w.h.p. takes \(\tilde{O}(n^{2-\frac{\alpha}{f+1}})\cdot{}O(\log n/\varepsilon)^{f+2}\) space and has an \(O(n^\alpha/\varepsilon^2)\) query time. The time to build the oracle is \(\tilde{O}(mn^{2-\frac{\alpha}{f+1}})\cdot{}O(\log n/\varepsilon)^{f+1}\). We also give an improved construction for graphs with diameter at most \(D\). For any positive integer \(k\), we devise an \(f\)-DSO with stretch \(2k-1\) that w.h.p. takes \(O(D^{f+o(1)}n^{1+1/k})\) space and has \(\tilde{O}(D^o(1)})\) query time, with a preprocessing time of \(O(D^{f+o(1)}mn^{1/k})\). Chechik, Cohen, Fiat, and Kaplan [SODA 2017] devised an \(f\)-DSO with stretch \(1{+}\varepsilon\) and preprocessing time \(O(n^{5+o(1)}/\varepsilon^f)\), albeit with a super-quadratic space requirement. We show how to reduce their preprocessing time to \(O(mn^{2+o(1)}/\varepsilon^f)\).
@article{bil2024approximate, abstract = {An \(f\)-edge fault-tolerant distance sensitive oracle (\(f\)-DSO) with stretch \(\sigma\ge{}1\) is a data structure that preprocesses a given undirected, unweighted graph \(G\) with \(n\) vertices and \(m\) edges, and a positive integer \(f\). When queried with a pair of vertices \(s,t\) and a set \(F\) of at most \(f\) edges, it returns a \(\sigma\)-approximation of the \(s\)-\(t\)-distance in \(G-F\). We study \(f\)-DSOs that take subquadratic space. Thorup and Zwick [JACM 2005] showed that this is only possible for \(\sigma \ge 3\). We present, for any constant \(f\ge{}1\) and \(\alpha\in(0,\frac{1}{2})\), and any \(\varepsilon>0\), a randomized \(f\)-DSO with stretch \( 3+\varepsilon\) that w.h.p.\ takes \(\tilde{O}(n^{2-\frac{\alpha}{f+1}})\cdot{}O(\log n/\varepsilon)^{f+2}\) space and has an \(O(n^\alpha/\varepsilon^2)\) query time. The time to build the oracle is \(\tilde{O}(mn^{2-\frac{\alpha}{f+1}})\cdot{}O(\log n/\varepsilon)^{f+1}\). We also give an improved construction for graphs with diameter at most \(D\). For any positive integer \(k\), we devise an \(f\)-DSO with stretch \(2k-1\) that w.h.p.\ takes \(O(D^{f+o(1)}n^{1+1/k})\) space and has \(\tilde{O}(D^{o(1)})\) query time, with a preprocessing time of \(O(D^{f+o(1)}mn^{1/k})\). Chechik, Cohen, Fiat, and Kaplan [SODA 2017] devised an \(f\)-DSO with stretch \(1{+}\varepsilon\) and preprocessing time \(O(n^{5+o(1)}/\varepsilon^f)\), albeit with a super-quadratic space requirement. We show how to reduce their preprocessing time to \(O(mn^{2+o(1)}/\varepsilon^f)\).}, author = {Bilò, Davide and Chechik, Shiri and Choudhary, Keerti and Cohen, Sarel and Friedrich, Tobias and Krogmann, Simon and Schirneck, Martin}, journal = {TheoretiCS}, keywords = {sarelcohen theoretics tobiasfriedrich year2024 simonkrogmann martinschirneck}, title = {Approximate Distance Sensitivity Oracles in Subquadratic Space}, volume = 3, year = 2024 }

Antipov, Denis; Kötzing, Timo; Radhakrishnan, Aishwarya Greedy versus Curious Parent Selection for Multi-Objective Evolutionary Algorithms 2024
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From the literature we know that simple evolutionary multi- objective algorithms can optimize the classic two-objective test functions OneMinMax and CountingOnesCountingZeroes in O(n^2 log n) expected time. We extend this result to any pair of generalized OneMax functions and show that, if the optima of the two functions are d apart, then (G)SEMO has an expected optimization time of O(dn log(n)). In an attempt to achieve better optimization times, some algorithms consider parent selection. We show that parent selection based on the curiosity-based novelty search can improve the optimization time to O(n^2) on OneMinMax. By contrast, we show that greedy parent selection schemes can be trapped with an incomplete Pareto front for superpolynomial time. Finally, we provide experimental results on the two-objective optimization of linear functions.
@conference{antipov2024greedy, abstract = {From the literature we know that simple evolutionary multi- objective algorithms can optimize the classic two-objective test functions OneMinMax and CountingOnesCountingZeroes in O(n^2 log n) expected time. We extend this result to any pair of generalized OneMax functions and show that, if the optima of the two functions are d apart, then (G)SEMO has an expected optimization time of O(dn log(n)). In an attempt to achieve better optimization times, some algorithms consider parent selection. We show that parent selection based on the curiosity-based novelty search can improve the optimization time to O(n^2) on OneMinMax. By contrast, we show that greedy parent selection schemes can be trapped with an incomplete Pareto front for superpolynomial time. Finally, we provide experimental results on the two-objective optimization of linear functions.}, author = {Antipov, Denis and Kötzing, Timo and Radhakrishnan, Aishwarya}, keywords = {myown sys:relevantfor:ae aishwaryaradhakrishnan ppsn24 timokoetzing}, title = {Greedy versus Curious Parent Selection for Multi-Objective Evolutionary Algorithms}, year = 2024 }

Harder, Jonathan Gadea; Kötzing, Timo; Li, Xiaoyue; Radhakrishnan, Aishwarya; Ruff, Janosch Run Time Bounds for Integer-Valued OneMax FunctionsGenetic and Evolutionary Computation Conference (GECCO ’24) 2024
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@conference{2024bounds, author = {Harder, Jonathan Gadea and Kötzing, Timo and Li, Xiaoyue and Radhakrishnan, Aishwarya and Ruff, Janosch}, booktitle = {Genetic and Evolutionary Computation Conference (GECCO '24)}, keywords = {sys:relevantfor:ae aishwaryaradhakrishnan xiaoyueli timokoetzing janoschruff gecco year2024 jonathangadeaharder}, title = {Run Time Bounds for Integer-Valued OneMax Functions}, year = 2024 }

Cohen, Sarel; Kamma, Lior; Niklanovits, Aikaterini A New Approach for Approximating Directed Rooted Networks50th International Workshop on Graph-Theoretic Concepts in Computer Science 2024
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We consider the k-outconnected directed Steiner tree problem (k-DST). Given a directed edge-weighted graph G=(V,E,w), where \(V = \r\} \cup S \cup T\), and an integer k, the goal is to find a minimum cost subgraph of \($G$\) in which there are k edge-disjoint rt-paths for every terminal \(t \in T\). The problem is known to be NP-Hard. Furthermore,the question on whether a polynomial time, subpolynomial approximation algorithm exists for k-DST was answered negatively by Grandoni etal (2018), by proving an approximation hardness of \(\Omega(|T|/\log |T|)\) under NP\(\neq\)ZPP. Inspired by modern day applications, we focus on developing efficient algorithms for k-DST in graphs where terminals have out-degree 0, and furthermore constitute the vast majority in the graph. We provide the first approximation algorithm for k-DST on such graphs, in which the approximation ratio depends (primarily) on the size of S. We present a randomized algorithm that finds a solution of weight at most \(O(k|S| \log|T|)\) times the optimal weight, and with high probability runs in polynomial time.
@inproceedings{cohen2024approach, abstract = {We consider the k-outconnected directed Steiner tree problem (k-DST). Given a directed edge-weighted graph G=(V,E,w), where \(V = \{r\} \cup S \cup T\), and an integer k, the goal is to find a minimum cost subgraph of $G$ in which there are k edge-disjoint rt-paths for every terminal \(t \in T\). The problem is known to be NP-Hard. Furthermore,the question on whether a polynomial time, subpolynomial approximation algorithm exists for k-DST was answered negatively by Grandoni \etal (2018), by proving an approximation hardness of \(\Omega(|T|/\log |T|)\) under NP\(\neq\)ZPP. Inspired by modern day applications, we focus on developing efficient algorithms for k-DST in graphs where terminals have out-degree 0, and furthermore constitute the vast majority in the graph. We provide the first approximation algorithm for k-DST on such graphs, in which the approximation ratio depends (primarily) on the size of S. We present a randomized algorithm that finds a solution of weight at most \(O(k|S| \log|T|)\) times the optimal weight, and with high probability runs in polynomial time.}, author = {Cohen, Sarel and Kamma, Lior and Niklanovits, Aikaterini}, editor = {"Kráľ, Daniel" and "Milanič, Martin"}, journal = {50th International Workshop on Graph-Theoretic Concepts in Computer Science}, keywords = {sarelcohen sys:relevantfor:ae aikaterininiklanovits year2024 DirectedSteinerTree wg}, title = {A New Approach for Approximating Directed Rooted Networks}, year = 2024 }

Horev, Yinon; Shay, Shiraz; Cohen, Sarel; Friedrich, Tobias; Issac, Davis; Kamma, Lior; Niklanovits, Aikaterini; Simonov, Kirill A Contraction Tree SAT Encoding for Computing Twin-WidthAdvances in Knowledge Discovery and Data Mining 2024
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Twin-width is a structural width parameter and matrix invariant introduced by Bonnet et al. [FOCS 2020], that has been gaining attention due to its various fields of applications. In this paper, inspired by the SAT approach of Schidler and Szeider [ALENEX 2022], we provide a new SAT encoding for computing twin-width. The encoding aims to encode the contraction sequence as a binary tree. The asymptotic size of the formula under our encoding is smaller than in the state-of-the-art relative encoding of Schidler and Szeider. We also conduct an experimental study, comparing the performance of the new encoding and the relative encoding.
@inproceedings{horev2024contraction, abstract = {Twin-width is a structural width parameter and matrix invariant introduced by Bonnet et al. [FOCS 2020], that has been gaining attention due to its various fields of applications. In this paper, inspired by the SAT approach of Schidler and Szeider [ALENEX 2022], we provide a new SAT encoding for computing twin-width. The encoding aims to encode the contraction sequence as a binary tree. The asymptotic size of the formula under our encoding is smaller than in the state-of-the-art relative encoding of Schidler and Szeider. We also conduct an experimental study, comparing the performance of the new encoding and the relative encoding.}, author = {Horev, Yinon and Shay, Shiraz and Cohen, Sarel and Friedrich, Tobias and Issac, Davis and Kamma, Lior and Niklanovits, Aikaterini and Simonov, Kirill}, booktitle = {Advances in Knowledge Discovery and Data Mining}, keywords = {sarelcohen yinonhorev davisissac kirillsimonov aikaterininiklanovits tobiasfriedrich year2024 shirazshay liorkamma pakdd}, month = {April 2024}, publisher = {Springer, Singapore}, title = {A Contraction Tree SAT Encoding for Computing Twin-Width}, volume = 14646, year = 2024 }

Friedrich, Tobias; Göbel, Andreas; Klodt, Nicolas; Krejca, Martin S.; Pappik, Marcus The Irrelevance of Influencers: Information Diffusion with Re-Activation and Immunity Lasts Exponentially Long on Social Network ModelsAnnual AAAI Conference on Artificial Intelligence 2024
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Information diffusion models on networks are at the forefront of AI research. The dynamics of such models typically follow stochastic models from epidemiology, used to model not only infections but various phenomena, including the behavior of computer viruses and viral marketing campaigns. A core question in this setting is how to efficiently detect the most influential vertices in the host graph such that the infection survives the longest. In processes that incorporate re-infection of the vertices, such as the SIS process, theoretical studies identify parameter thresholds where the survival time of the process rapidly transitions from logarithmic to super-polynomial. These results contradict the intuition that the starting configuration is relevant, since the process will always either die out fast or survive almost indefinitely. A shortcoming of these results is that models incorporating short-term immunity (or creative advertisement fatigue) have not been subjected to such a theoretical analysis so far. We reduce this gap in the literature by studying the SIRS process, a more realistic model, which besides re-infection additionally incorporates short-term immunity. On complex network models, we identify parameter regimes for which the process survives exponentially long, and we get a tight threshold for random graphs. Underlying these results is our main technical contribution, showing a threshold behavior for the survival time of the SIRS process on graphs with large expander subgraphs, such as social network models.
@inproceedings{friedrich2024irrelevance, abstract = {Information diffusion models on networks are at the forefront of AI research. The dynamics of such models typically follow stochastic models from epidemiology, used to model not only infections but various phenomena, including the behavior of computer viruses and viral marketing campaigns. A core question in this setting is how to efficiently detect the most influential vertices in the host graph such that the infection survives the longest. In processes that incorporate re-infection of the vertices, such as the SIS process, theoretical studies identify parameter thresholds where the survival time of the process rapidly transitions from logarithmic to super-polynomial. These results contradict the intuition that the starting configuration is relevant, since the process will always either die out fast or survive almost indefinitely. A shortcoming of these results is that models incorporating short-term immunity (or creative advertisement fatigue) have not been subjected to such a theoretical analysis so far. We reduce this gap in the literature by studying the SIRS process, a more realistic model, which besides re-infection additionally incorporates short-term immunity. On complex network models, we identify parameter regimes for which the process survives exponentially long, and we get a tight threshold for random graphs. Underlying these results is our main technical contribution, showing a threshold behavior for the survival time of the SIRS process on graphs with large expander subgraphs, such as social network models.}, author = {Friedrich, Tobias and Göbel, Andreas and Klodt, Nicolas and Krejca, Martin S. and Pappik, Marcus}, booktitle = {Annual AAAI Conference on Artificial Intelligence}, keywords = {nicolasklodt marcuspappik martinskrejca andreasgoebel tobiasfriedrich aaai year2024}, title = {The Irrelevance of Influencers: Information Diffusion with Re-Activation and Immunity Lasts Exponentially Long on Social Network Models}, year = 2024 }

Angrick, Sebastian; Bals, Ben; Friedrich, Tobias; Gawendowicz, Hans; Hastrich, Niko; Klodt, Nicolas; Lenzner, Pascal; Schmidt, Jonas; Skretas, George; Wells, Armin How to Reduce Temporal Cliques to Find Sparse SpannersEuropean Symposium on Algorithms (ESA) 2024
[ BibTeX ]
 
@inproceedings{angrick2024reduce, author = {Angrick, Sebastian and Bals, Ben and Friedrich, Tobias and Gawendowicz, Hans and Hastrich, Niko and Klodt, Nicolas and Lenzner, Pascal and Schmidt, Jonas and Skretas, George and Wells, Armin}, booktitle = {European Symposium on Algorithms (ESA)}, keywords = {hansgawendowicz nicolasklodt esa tobiasfriedrich year2024 pascallenzner georgeskretas}, title = {How to Reduce Temporal Cliques to Find Sparse Spanners}, year = 2024 }

Constantinescu, Andrei; Lenzner, Pascal; Reiffenhäuser, Rebecca; Schmand, Daniel; Varricchio, Giovanna Solving Woeginger’s Hiking Problem: Wonderful Partitions in Anonymous Hedonic GamesInternational Colloquium on Automata, Languages and Programming (ICALP) 2024
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
A decade ago, Gerhard Woeginger posed an open problem that became well-known as "Woeginger’s Hiking Problem": Consider a group of n people that want to go hiking; everyone expresses preferences over the size of their hiking group in the form of an interval between 1 and n. Is it possible to efficiently assign the n people to a set of hiking subgroups so that every person approves the size of their assigned subgroup? The problem is also known as efficiently deciding if an instance of an anonymous Hedonic Game with interval approval preferences admits a wonderful partition. We resolve the open problem in the affirmative by presenting an O(n⁵) time algorithm for Woeginger’s Hiking Problem. Our solution is based on employing a dynamic programming approach for a specific rectangle stabbing problem from computational geometry. Moreover, we propose natural, more demanding extensions of the problem, e.g., maximizing the number of satisfied participants and variants with single-peaked preferences, and show that they are also efficiently solvable. Last but not least, we employ our solution to efficiently compute a partition that maximizes the egalitarian welfare for anonymous single-peaked Hedonic Games.
@inproceedings{constantinescu2024solving, abstract = {A decade ago, Gerhard Woeginger posed an open problem that became well-known as "Woeginger’s Hiking Problem": Consider a group of n people that want to go hiking; everyone expresses preferences over the size of their hiking group in the form of an interval between 1 and n. Is it possible to efficiently assign the n people to a set of hiking subgroups so that every person approves the size of their assigned subgroup? The problem is also known as efficiently deciding if an instance of an anonymous Hedonic Game with interval approval preferences admits a wonderful partition. We resolve the open problem in the affirmative by presenting an O(n⁵) time algorithm for Woeginger’s Hiking Problem. Our solution is based on employing a dynamic programming approach for a specific rectangle stabbing problem from computational geometry. Moreover, we propose natural, more demanding extensions of the problem, e.g., maximizing the number of satisfied participants and variants with single-peaked preferences, and show that they are also efficiently solvable. Last but not least, we employ our solution to efficiently compute a partition that maximizes the egalitarian welfare for anonymous single-peaked Hedonic Games.}, author = {Constantinescu, Andrei and Lenzner, Pascal and Reiffenhäuser, Rebecca and Schmand, Daniel and Varricchio, Giovanna}, booktitle = {International Colloquium on Automata, Languages and Programming (ICALP)}, keywords = {year2024 icalp pascallenzner}, title = {Solving Woeginger's Hiking Problem: Wonderful Partitions in Anonymous Hedonic Games}, year = 2024 }

Friedrich, Tobias; Göbel, Andreas; Katzmann, Maximilian; Schiller, Leon Real-World Networks Are Low-Dimensional: Theoretical and Practical AssessmentInternational Joint Conference on Artificial Intelligence (IJCAI) 2024
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Recent empirical evidence suggests that real-world networks have very low underlying dimensionality. We provide a theoretical explanation for this phenomenon as well as develop a linear-time algorithm for detecting the underlying dimensionality of such networks. Our theoretical analysis considers geometric inhomogeneous random graphs (GIRGs), a geometric random graph model, which captures a variety of properties observed in real-world networks. These properties include a heterogeneous degree distribution and non-vanishing clustering coefficient, which is the probability that two random neighbors of a vertex are adjacent. Our first result shows that the clustering coefficient of GIRGs scales inverse exponentially with respect to the number of dimensions d, when the latter is at most logarithmic in n, the number of vertices. Hence, for a GIRG to behave like many real-world networks and have a non-vanishing clustering coefficient, it must come from a geometric space of o(log n) dimensions. Our analysis on GIRGs allows us to obtain a linear-time algorithm for determining the dimensionality of a network. Our algorithm bridges the gap between theory and practice, as it comes with a rigorous proof of correctness and yields results comparable to prior empirical approaches, as indicated by our experiments on real-world instances. The efficiency of our algorithm makes it applicable to very large data-sets. We conclude that very low dimensionalities (from 1 to 10) are needed to explain properties of real-world networks.
@inproceedings{friedrich2024realworld, abstract = {Recent empirical evidence suggests that real-world networks have very low underlying dimensionality. We provide a theoretical explanation for this phenomenon as well as develop a linear-time algorithm for detecting the underlying dimensionality of such networks. Our theoretical analysis considers geometric inhomogeneous random graphs (GIRGs), a geometric random graph model, which captures a variety of properties observed in real-world networks. These properties include a heterogeneous degree distribution and non-vanishing clustering coefficient, which is the probability that two random neighbors of a vertex are adjacent. Our first result shows that the clustering coefficient of GIRGs scales inverse exponentially with respect to the number of dimensions d, when the latter is at most logarithmic in n, the number of vertices. Hence, for a GIRG to behave like many real-world networks and have a non-vanishing clustering coefficient, it must come from a geometric space of o(log n) dimensions. Our analysis on GIRGs allows us to obtain a linear-time algorithm for determining the dimensionality of a network. Our algorithm bridges the gap between theory and practice, as it comes with a rigorous proof of correctness and yields results comparable to prior empirical approaches, as indicated by our experiments on real-world instances. The efficiency of our algorithm makes it applicable to very large data-sets. We conclude that very low dimensionalities (from 1 to 10) are needed to explain properties of real-world networks.}, author = {Friedrich, Tobias and Göbel, Andreas and Katzmann, Maximilian and Schiller, Leon}, booktitle = {International Joint Conference on Artificial Intelligence (IJCAI)}, keywords = {ijcai andreasgoebel tobiasfriedrich year2024}, title = {Real-World Networks Are Low-Dimensional: Theoretical and Practical Assessment}, year = 2024 }

Krogmann, Simon; Lenzner, Pascal; Skopalik, Alexander; Uetz, Marc; Vos, Marnix C. Equilibria in Two-Stage Facility Location with Atomic ClientsInternational Joint Conference on Artificial Intelligence (IJCAI) 2024: 2842–2850
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
We consider competitive facility location as a two-stage multi-agent system with two types of clients. For a given host graph with weighted clients on the vertices, first facility agents strategically select vertices for opening their facilities. Then, the clients strategically select which of the opened facilities in their neighborhood to patronize. Facilities want to attract as much client weight as possible, clients want to minimize congestion on the chosen facility. All recently studied versions of this model assume that clients can split their weight strategically. We consider clients with unsplittable weights, but allow mixed strategies. So clients may randomize over which facility to patronize. Besides modeling a natural client behavior, this subtle change yields drastic changes, e.g., for a given facility placement, qualitatively different client equilibria are possible. As our main result, we show that pure subgame perfect equilibria always exist if all client weights are identical. For this, we use a novel potential function argument, employing a hierarchical classification of the clients and sophisticated rounding in each step. In contrast, for non-identical clients, we show that deciding the existence of even approximately stable states is computationally intractable. On the positive side, we give a tight bound of 2 on the price of anarchy which implies high social welfare of equilibria, if they exist.
@inproceedings{krogmann2024equilibria, abstract = {We consider competitive facility location as a two-stage multi-agent system with two types of clients. For a given host graph with weighted clients on the vertices, first facility agents strategically select vertices for opening their facilities. Then, the clients strategically select which of the opened facilities in their neighborhood to patronize. Facilities want to attract as much client weight as possible, clients want to minimize congestion on the chosen facility. All recently studied versions of this model assume that clients can split their weight strategically. We consider clients with unsplittable weights, but allow mixed strategies. So clients may randomize over which facility to patronize. Besides modeling a natural client behavior, this subtle change yields drastic changes, e.g., for a given facility placement, qualitatively different client equilibria are possible. As our main result, we show that pure subgame perfect equilibria always exist if all client weights are identical. For this, we use a novel potential function argument, employing a hierarchical classification of the clients and sophisticated rounding in each step. In contrast, for non-identical clients, we show that deciding the existence of even approximately stable states is computationally intractable. On the positive side, we give a tight bound of 2 on the price of anarchy which implies high social welfare of equilibria, if they exist.}, author = {Krogmann, Simon and Lenzner, Pascal and Skopalik, Alexander and Uetz, Marc and Vos, Marnix C.}, booktitle = {International Joint Conference on Artificial Intelligence (IJCAI)}, keywords = {ijcai year2024 simonkrogmann pascallenzner}, pages = {2842-2850}, title = {Equilibria in Two-Stage Facility Location with Atomic Clients}, year = 2024 }

Casel, Katrin; Friedrich, Tobias; Niklanovits, Aikaterini; Simonov, Kirill; Zeif, Ziena Combining Crown Structures for Vulnerability MeasuresInternational Symposium on Parameterized and Exact Computation (IPEC) 2024
Best Paper Award
[ Abstract ] [ BibTeX ]
 
Over the past decades, various metrics have emerged in graph theory to grasp the complex nature of network vulnerability. In this paper, we study two specific measures: (weighted) vertex integrity (wVI) and (weighted) component order connectivity (wCOC). These measures not only evaluate the number of vertices required to decompose a graph into fragments, but also take into account the size of the largest remaining component. The main focus of our paper is on kernelization algorithms tailored to both measures. We capitalize on the structural attributes inherent in different crown decompositions, strategically combining them to introduce novel kernelization algorithms that advance the current state of the field. In particular, we extend the scope of the balanced crown decomposition provided by Casel et al.~\cite{DBLP:conf/esa/Casel0INZ21 and expand the applicability of crown decomposition techniques. In summary, we improve the vertex kernel of VI from \(p^3\) to \(p^2\), and of wVI from \(p^3\) to \(3(p^2 + p^1.5 p_{\ell})\), where \(p_{\ell} < p\) represents the weight of the heaviest component after removing a solution. For wCOC we improve the vertex kernel from \(\mathcal{O(k^2W + kW^2)\) to \(3\mu(k + \sqrt{\mu}W)\), where \(mu = \max(k,W)\). We also give a combinatorial algorithm that provides a \(2kW\) vertex kernel in fixed-parameter tractable time when parameterized by \(r\), where \(r \leq k\) is the size of a maximum \((W+1)\)-packing. We further show that the algorithm computing the \(2kW\) vertex kernel for COC can be transformed into a polynomial algorithm for two special cases, namely when \(W=1\), which corresponds to the well-known vertex cover problem, and for claw-free graphs. In particular, we show a new way to obtain a \($2k$\) vertex kernel (or to obtain a 2-approximation) for the vertex cover problem by only using crown structures.
@inproceedings{casel2024combining, abstract = {Over the past decades, various metrics have emerged in graph theory to grasp the complex nature of network vulnerability. In this paper, we study two specific measures: (weighted) vertex integrity (wVI) and (weighted) component order connectivity (wCOC). These measures not only evaluate the number of vertices required to decompose a graph into fragments, but also take into account the size of the largest remaining component. The main focus of our paper is on kernelization algorithms tailored to both measures. We capitalize on the structural attributes inherent in different crown decompositions, strategically combining them to introduce novel kernelization algorithms that advance the current state of the field. In particular, we extend the scope of the balanced crown decomposition provided by Casel et al.&nbsp;\cite{DBLP:conf/esa/Casel0INZ21} and expand the applicability of crown decomposition techniques. In summary, we improve the vertex kernel of VI from \(p^3\) to \(p^2\), and of wVI from \(p^3\) to \(3(p^2 + {p}^{1.5} p_{\ell})\), where \(p_{\ell} < p\) represents the weight of the heaviest component after removing a solution. For wCOC we improve the vertex kernel from \(\mathcal{O}(k^2W + kW^2)\) to \(3\mu(k + \sqrt{\mu}W)\), where \(\mu = \max(k,W)\). We also give a combinatorial algorithm that provides a \(2kW\) vertex kernel in fixed-parameter tractable time when parameterized by \(r\), where \(r \leq k\) is the size of a maximum \((W+1)\)-packing. We further show that the algorithm computing the \(2kW\) vertex kernel for COC can be transformed into a polynomial algorithm for two special cases, namely when \(W=1\), which corresponds to the well-known vertex cover problem, and for claw-free graphs. In particular, we show a new way to obtain a $2k$ vertex kernel (or to obtain a 2-approximation) for the vertex cover problem by only using crown structures.}, author = {Casel, Katrin and Friedrich, Tobias and Niklanovits, Aikaterini and Simonov, Kirill and Zeif, Ziena}, booktitle = {International Symposium on Parameterized and Exact Computation (IPEC)}, keywords = {zienazeif ipec katrincasel kirillsimonov aikaterininiklanovits tobiasfriedrich year2024}, note = {Best Paper Award}, title = {Combining Crown Structures for Vulnerability Measures}, year = 2024 }

Andreev, Nikita; Bliznets, Ivan; Kundu, Madhumita; Saurabh, Saket; Tripathi, Vikash; Verma, Shaily Parameterized Complexity of Paired DominationInternational Workshop on Combinatorial Algorithms (IWOCA) 2024: 523–536
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
The Paired Domination problem is one of the well-studied variants of the classical Dominating Set problem. In a graph \(G\) on \(n\) vertices, a dominating set \(D\) (set of vertices such that \(N[D]=V(G)\)) is called a paired dominating set of \(G\), if \(G[D]\) has perfect matching. In the Paired Domination problem, given a graph \(G\) and a positive integer \(k\), the task is to check whether \(G\) has a paired dominating set of size at most \(k\). The problem is a variant of the Dominating Set problem, and hence inherits most of the hardness of the Dominating Set problem; however, the same cannot be said about the algorithmic results. In this paper, we study the problem from the perspective of parameterized complexity, both from solution and structural parameterization, and obtain the following results. 1. We design an (non-trivial) exact exponential algorithm running in time \(1.7159^n\). 2. It admits Strong Exponential Time Hypothesis (SETH) optimal algorithm parameterized by the treewidth \(tw\) of the graph \(G\). The algorithm runs in time \(4^{tw}n^O(1)}\) and unless SETH fails, there is no algorithm running in time \((4-\epsilon)^twn^O(1)}\) for any \(\epsilon >0\). 3. We design an algorithm parameterized by the distance to cluster graphs. We complement this result by proving that the problem does not admit a polynomial kernel under this parameterization and under parameterization by vertex cover number. 4. Paired Domination admits a polynomial kernel on graphs that exclude a biclique \(K_{i,j}\). 5. We also prove that one of the counting versions of Paired Domination parameterized by cliquewidth admits \(n^{2cw+O(1)}\) time algorithm parameterized by cliquewidth (\(cw\)). However, it does not admit an FPT algorithm unless #SETH is false.
@inproceedings{andreev2024parameterized, abstract = {The Paired Domination problem is one of the well-studied variants of the classical Dominating Set problem. In a graph \(G\) on \(n\) vertices, a dominating set \(D\) (set of vertices such that \(N[D]=V(G)\)) is called a paired dominating set of \(G\), if \(G[D]\) has perfect matching. In the Paired Domination problem, given a graph \(G\) and a positive integer \(k\), the task is to check whether \(G\) has a paired dominating set of size at most \(k\). The problem is a variant of the Dominating Set problem, and hence inherits most of the hardness of the Dominating Set problem; however, the same cannot be said about the algorithmic results. In this paper, we study the problem from the perspective of parameterized complexity, both from solution and structural parameterization, and obtain the following results. 1. We design an (non-trivial) exact exponential algorithm running in time \(1.7159^n\). 2. It admits Strong Exponential Time Hypothesis (SETH) optimal algorithm parameterized by the treewidth \(tw\) of the graph \(G\). The algorithm runs in time \(4^{tw}n^{O(1)}\) and unless SETH fails, there is no algorithm running in time \((4-\epsilon)^{tw}n^{O(1)}\) for any \(\epsilon >0\). 3. We design an algorithm parameterized by the distance to cluster graphs. We complement this result by proving that the problem does not admit a polynomial kernel under this parameterization and under parameterization by vertex cover number. 4. Paired Domination admits a polynomial kernel on graphs that exclude a biclique \(K_{i,j}\). 5. We also prove that one of the counting versions of Paired Domination parameterized by cliquewidth admits \(n^{2cw+O(1)}\) time algorithm parameterized by cliquewidth (\(cw\)). However, it does not admit an FPT algorithm unless #SETH is false.}, author = {Andreev, Nikita and Bliznets, Ivan and Kundu, Madhumita and Saurabh, Saket and Tripathi, Vikash and Verma, Shaily}, booktitle = {International Workshop on Combinatorial Algorithms (IWOCA)}, keywords = {iwoca sys:relevantfor:ae shailyverma year2024}, organization = {Springer}, pages = {523&ndash;536}, title = {Parameterized Complexity of Paired Domination}, year = 2024 }

Göbel, Andreas; Goldberg, Leslie Ann; Roth, Marc The Weisfeiler-Leman Dimension of Conjunctive QueriesSymposium on Principles of Database Systems (PODS) 2024
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
The Weisfeiler-Leman (WL) dimension of a graph parameter f is the minimum k such that, if G1 and G2 are indistinguishable by the k-dimensional WL-algorithm then f(G1)=f(G2). The WL-dimension of f is ∞ if no such k exists. We study the WL-dimension of graph parameters characterised by the number of answers from a fixed conjunctive query to the graph. Given a conjunctive query φ, we quantify the WL-dimension of the function that maps every graph G to the number of answers of φ in G. The works of Dvorák (J. Graph Theory 2010), Dell, Grohe, and Rattan (ICALP 2018), and Neuen (ArXiv 2023) have answered this question for full conjunctive queries, which are conjunctive queries without existentially quantified variables. For such queries φ, the WL-dimension is equal to the treewidth of the Gaifman graph of φ. In this work, we give a characterisation that applies to all conjunctive qureies. Given any conjunctive query φ, we prove that its WL-dimension is equal to the semantic extension width sew(φ), a novel width measure that can be thought of as a combination of the treewidth of φ and its quantified star size, an invariant introduced by Durand and Mengel (ICDT 2013) describing how the existentially quantified variables of φ are connected with the free variables. Using the recently established equivalence between the WL-algorithm and higher-order Graph Neural Networks (GNNs) due to Morris et al. (AAAI 2019), we obtain as a consequence that the function counting answers to a conjunctive query φ cannot be computed by GNNs of order smaller than sew(φ).
@inproceedings{gobel2024weisfeilerleman, abstract = {The Weisfeiler-Leman (WL) dimension of a graph parameter f is the minimum k such that, if G1 and G2 are indistinguishable by the k-dimensional WL-algorithm then f(G1)=f(G2). The WL-dimension of f is ∞ if no such k exists. We study the WL-dimension of graph parameters characterised by the number of answers from a fixed conjunctive query to the graph. Given a conjunctive query φ, we quantify the WL-dimension of the function that maps every graph G to the number of answers of φ in G. The works of Dvorák (J. Graph Theory 2010), Dell, Grohe, and Rattan (ICALP 2018), and Neuen (ArXiv 2023) have answered this question for full conjunctive queries, which are conjunctive queries without existentially quantified variables. For such queries φ, the WL-dimension is equal to the treewidth of the Gaifman graph of φ. In this work, we give a characterisation that applies to all conjunctive qureies. Given any conjunctive query φ, we prove that its WL-dimension is equal to the semantic extension width sew(φ), a novel width measure that can be thought of as a combination of the treewidth of φ and its quantified star size, an invariant introduced by Durand and Mengel (ICDT 2013) describing how the existentially quantified variables of φ are connected with the free variables. Using the recently established equivalence between the WL-algorithm and higher-order Graph Neural Networks (GNNs) due to Morris et al. (AAAI 2019), we obtain as a consequence that the function counting answers to a conjunctive query φ cannot be computed by GNNs of order smaller than sew(φ).}, author = {Göbel, Andreas and Goldberg, Leslie Ann and Roth, Marc}, booktitle = {Symposium on Principles of Database Systems (PODS)}, keywords = {sys:relevantfor:ae andreasgoebel pods year2024}, title = {The Weisfeiler-Leman Dimension of Conjunctive Queries}, year = 2024 }

Li, Xiaoyue; Kötzing, Timo Algorithm Performance Comparison for Integer-Valued OneMaxGenetic and Evolutionary Computation Conference (GECCO ’24 Companion) 2024: 407–410
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Recently, several continuous-domain optimizers have been employed to solve mixed-integer black box optimization (MI-BBO) problems by adjusting them to handle the discrete variables as well. In this work we want to compare how these adjusted algorithms perform on purely discrete variables when compared with algorithms designed to handle discrete domains. We use the algorithm RLS from the literature, which was analyzed theoretically on a specific problem class. We experimentally optimize the parameters a and b for further analysis. Second, we make a comprehensive comparison of RLS with algorithms from the continuous domain on a generalization of OneMax to Z. We find that RLS shows better performance on this discrete benchmark functions than the other algorithms. Overall, these results show that adaptations of continuous algorithms are not suited for MI-BBO problems, and that research combining the strengths of both approaches is more promising.
@inproceedings{li2024algorithm, abstract = {Recently, several continuous-domain optimizers have been employed to solve mixed-integer black box optimization (MI-BBO) problems by adjusting them to handle the discrete variables as well. In this work we want to compare how these adjusted algorithms perform on purely discrete variables when compared with algorithms designed to handle discrete domains. We use the algorithm RLS from the literature, which was analyzed theoretically on a specific problem class. We experimentally optimize the parameters a and b for further analysis. Second, we make a comprehensive comparison of RLS with algorithms from the continuous domain on a generalization of OneMax to Z. We find that RLS shows better performance on this discrete benchmark functions than the other algorithms. Overall, these results show that adaptations of continuous algorithms are not suited for MI-BBO problems, and that research combining the strengths of both approaches is more promising.}, address = {New York, NY, USA}, author = {Li, Xiaoyue and Kötzing, Timo}, booktitle = {Proceedings of the Genetic and Evolutionary Computation Conference Companion}, journal = {Genetic and Evolutionary Computation Conference (GECCO ’24 Companion)}, keywords = {comparison xiaoyueli timokoetzing gecco year2024 performance}, month = {July}, pages = {407–410}, publisher = {Association for Computing Machinery}, series = {GECCO '24 Companion}, title = {Algorithm Performance Comparison for Integer-Valued OneMax}, year = 2024 }

Neubert, Stefan; Casel, Katrin Incremental Ordering for Scheduling ProblemsProceedings of the International Conference on Automated Planning and Scheduling 2024: 405–413
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Given an instance of a scheduling problem where we want to start executing jobs as soon as possible, it is advantageous if a scheduling algorithm emits the first parts of its solution early, in particular before the algorithm completes its work. Therefore, in this position paper, we analyze core scheduling problems in regards to their enumeration complexity, i.e. the computation time to the first emitted schedule entry (preprocessing time) and the worst case time between two consecutive parts of the solution (delay). Specifically, we look at scheduling instances that reduce to ordering problems. We apply a known incremental sorting algorithm for scheduling strategies that are at their core comparison-based sorting algorithms and translate corresponding upper and lower complexity bounds to the scheduling setting. For instances with n jobs and a precedence DAG with maximum degree Δ, we incrementally build a topological ordering with O(n) preprocessing and O(Δ) delay. We prove a matching lower bound and show with an adversary argument that the delay lower bound holds even in case the DAG has constant average degree and the ordering is emitted out-of-order in the form of insert operations. We complement our theoretical results with experiments that highlight the improved time-to-first-output and discuss research opportunities for similar incremental approaches for other scheduling problems.
@inproceedings{neubert2024incremental, abstract = {Given an instance of a scheduling problem where we want to start executing jobs as soon as possible, it is advantageous if a scheduling algorithm emits the first parts of its solution early, in particular before the algorithm completes its work. Therefore, in this position paper, we analyze core scheduling problems in regards to their enumeration complexity, i.e. the computation time to the first emitted schedule entry (preprocessing time) and the worst case time between two consecutive parts of the solution (delay). Specifically, we look at scheduling instances that reduce to ordering problems. We apply a known incremental sorting algorithm for scheduling strategies that are at their core comparison-based sorting algorithms and translate corresponding upper and lower complexity bounds to the scheduling setting. For instances with n jobs and a precedence DAG with maximum degree Δ, we incrementally build a topological ordering with O(n) preprocessing and O(Δ) delay. We prove a matching lower bound and show with an adversary argument that the delay lower bound holds even in case the DAG has constant average degree and the ordering is emitted out-of-order in the form of insert operations. We complement our theoretical results with experiments that highlight the improved time-to-first-output and discuss research opportunities for similar incremental approaches for other scheduling problems.}, author = {Neubert, Stefan and Casel, Katrin}, booktitle = {Proceedings of the International Conference on Automated Planning and Scheduling}, keywords = {katrincasel year2024 stefanneubert icaps}, month = {may}, number = 1, pages = {405-413}, publisher = {AAAI Press}, title = {Incremental Ordering for Scheduling Problems}, volume = 34, year = 2024 }

Fomin, Fedor V.; Golovach, Petr A.; Sagunov, Danil; Simonov, Kirill Tree Containment Above Minimum Degree is FPTSymposium on Discrete Algorithms (SODA) 2024: 366–376
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Abstract According to the classic Chvatal's Lemma from 1977, a graph of minimum degree \(\delta(G)\) contains every tree on \(\delta(G)+1\) vertices. Our main result is the following algorithmic “extension” of Chvatal's Lemma: For any \(n\)-vertex graph G, integer \(k\), and a tree \(T\) on at most \(\delta(G)+k\) vertices, deciding whether \(G\) contains a subgraph isomorphic to \(T\), can be done in time \(f(k) · n^\mathcal{O(1)}\) for some function \(f\) of \(k\) only. The proof of our main result is based on an interplay between extremal graph theory and parameterized algorithms. The full version of the paper can be accessed at https://arxiv.org/abs/2310.09678.
@inproceedings{fomin2024containment, abstract = {Abstract According to the classic Chvatal's Lemma from 1977, a graph of minimum degree \(\delta(G)\) contains every tree on \(\delta(G)+1\) vertices. Our main result is the following algorithmic “extension” of Chvatal's Lemma: For any \(n\)-vertex graph G, integer \(k\), and a tree \(T\) on at most \(\delta(G)+k\) vertices, deciding whether \(G\) contains a subgraph isomorphic to \(T\), can be done in time \(f(k) · n^{\mathcal{O}(1)}\) for some function \(f\) of \(k\) only. The proof of our main result is based on an interplay between extremal graph theory and parameterized algorithms. The full version of the paper can be accessed at https://arxiv.org/abs/2310.09678.}, author = {Fomin, Fedor V. and Golovach, Petr A. and Sagunov, Danil and Simonov, Kirill}, booktitle = {Symposium on Discrete Algorithms (SODA)}, keywords = {kirillsimonov year2024 soda}, pages = {366-376}, title = {Tree Containment Above Minimum Degree is FPT}, year = 2024 }

Friedrich, Tobias; Göbel, Andreas; Klodt, Nicolas; Krejca, Martin S.; Pappik, Marcus From Market Saturation to Social Reinforcement: Understanding the Impact of Non-Linearity in Information Diffusion ModelsThe 23rd International Conference on Autonomous Agents and Multi-Agent Systems 2024
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Diffusion of information in networks is at the core of many problems in AI. Common examples include the spread of ideas and rumors as well as marketing campaigns. Typically, information diffuses at a non-linear rate, for example, if markets become saturated or if users of social networks reinforce each other's opinions. Despite these characteristics, this area has seen little research, compared to the vast amount of results for linear models, which exhibit less complex dynamics. Especially, when considering the possibility of re-infection, no fully rigorous guarantees exist so far. We address this shortcoming by studying a very general non-linear diffusion model that captures saturation as well as reinforcement. More precisely, we consider a variant of the SIS model in which vertices get infected at a rate that scales polynomially in the number of their infected neighbors, weighted by an infection coefficient \(\lambda\). We give the first fully rigorous results for thresholds of \(\lambda\) at which the expected survival time becomes super-polynomial. For cliques we show that when the infection rate scales sub-linearly, the threshold only shifts by a poly-logarithmic factor, compared to the standard SIS model. In contrast, super-linear scaling changes the process considerably and shifts the threshold by a polynomial term. For stars, sub-linear and super-linear scaling behave similar and both shift the threshold by a polynomial factor. Our bounds are almost tight, as they are only apart by at most a poly-logarithmic factor from the lower thresholds, at which the expected survival time is logarithmic.
@inproceedings{friedrich2024market, abstract = {Diffusion of information in networks is at the core of many problems in AI. Common examples include the spread of ideas and rumors as well as marketing campaigns. Typically, information diffuses at a non-linear rate, for example, if markets become saturated or if users of social networks reinforce each other's opinions. Despite these characteristics, this area has seen little research, compared to the vast amount of results for linear models, which exhibit less complex dynamics. Especially, when considering the possibility of re-infection, no fully rigorous guarantees exist so far. We address this shortcoming by studying a very general non-linear diffusion model that captures saturation as well as reinforcement. More precisely, we consider a variant of the SIS model in which vertices get infected at a rate that scales polynomially in the number of their infected neighbors, weighted by an infection coefficient \(\lambda\). We give the first fully rigorous results for thresholds of \(\lambda\) at which the expected survival time becomes super-polynomial. For cliques we show that when the infection rate scales sub-linearly, the threshold only shifts by a poly-logarithmic factor, compared to the standard SIS model. In contrast, super-linear scaling changes the process considerably and shifts the threshold by a polynomial term. For stars, sub-linear and super-linear scaling behave similar and both shift the threshold by a polynomial factor. Our bounds are almost tight, as they are only apart by at most a poly-logarithmic factor from the lower thresholds, at which the expected survival time is logarithmic.}, author = {Friedrich, Tobias and Göbel, Andreas and Klodt, Nicolas and Krejca, Martin S. and Pappik, Marcus}, booktitle = {The 23rd International Conference on Autonomous Agents and Multi-Agent Systems}, keywords = {nicolasklodt marcuspappik martinskrejca andreasgoebel tobiasfriedrich aamas year2024}, title = {From Market Saturation to Social Reinforcement: Understanding the Impact of Non-Linearity in Information Diffusion Models}, year = 2024 }

2023

Friedrich, Tobias; Kötzing, Timo; Radhakrishnan, Aishwarya; Schiller, Leon; Schirneck, Martin; Tennigkeit, Georg; Wietheger, Simon Crossover for Cardinality Constrained OptimizationACM Transactions on Evolutionary Learning and Optimization 2023: 1–32
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
To understand better how and why crossover can benefit constrained optimization, we consider pseudo-Boolean functions with an upper bound \(B\) on the number of 1-bits allowed in the length-\(n\) bit string (i.e., a cardinality constraint). We investigate the natural translation of the OneMax test function to this setting, a linear function where \(B\) bits have a weight of \(1+ 1/n\) and the remaining bits have a weight of \(1\). Friedrich et al. [TCS 2020] gave a bound of \(\Theta(n^2)\) for the expected running time of 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 a \(1\) and a \(0\) simultaneously. The experimental literature proposes balanced operators, preserving the number of 1-bits, 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 for classic bit mutation. Crossover together with a simple island model gives running times of \(O(n^2 / \log n)\) (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 present an extensive analysis of different balanced crossover operators from the literature.
@article{friedrich2023crossover, abstract = {To understand better how and why crossover can benefit constrained optimization, we consider pseudo-Boolean functions with an upper bound \(B\) on the number of 1-bits allowed in the length-\(n\) bit string (i.e., a cardinality constraint). We investigate the natural translation of the OneMax test function to this setting, a linear function where \(B\) bits have a weight of \(1+ 1/n\) and the remaining bits have a weight of \(1\). Friedrich et al. [TCS 2020] gave a bound of \(\Theta(n^2)\) for the expected running time of 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 a \(1\) and a \(0\) simultaneously. The experimental literature proposes balanced operators, preserving the number of 1-bits, 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 for classic bit mutation. Crossover together with a simple island model gives running times of \(O(n^2 / \log n)\) (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 present an extensive analysis of 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}, journal = {ACM Transactions on Evolutionary Learning and Optimization}, keywords = {aishwaryaradhakrishnan telo timokoetzing simonwietheger tobiasfriedrich leonschiller year2023 georgtennigkeit martinschirneck}, pages = {1-32}, title = {Crossover for Cardinality Constrained Optimization}, volume = 3, year = 2023 }

Friedrich, Tobias; Gawendowicz, Hans; Lenzner, Pascal; Melnichenko, Anna Social Distancing Network CreationAlgorithmica 2023
[ 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. (in: PODC 2003, pp 347–351, 2003. https://doi.org/10.1145/872035.872088), where agents aim at being as central as possible in the created network. We look at two variants of network creation governed by social distancing. Firstly, a variant without connection restrictions, where we characterize optimal and equilibrium networks, and derive asymptotically tight bounds on the Price of Anarchy and Price of Stability. The second variant allows connection restrictions. 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 under social distancing the agents’ selfishness has a strong impact on the quality of the equilibria.
@article{friedrich2023social, 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. (in: PODC 2003, pp 347–351, 2003. https://doi.org/10.1145/872035.872088), where agents aim at being as central as possible in the created network. We look at two variants of network creation governed by social distancing. Firstly, a variant without connection restrictions, where we characterize optimal and equilibrium networks, and derive asymptotically tight bounds on the Price of Anarchy and Price of Stability. The second variant allows connection restrictions. 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 under social distancing the agents’ selfishness has a strong impact on the quality of the equilibria.}, author = {Friedrich, Tobias and Gawendowicz, Hans and Lenzner, Pascal and Melnichenko, Anna}, journal = {Algorithmica}, keywords = {hansgawendowicz algorithmica tobiasfriedrich year2023 annamelnichenko pascallenzner}, title = {Social Distancing Network Creation}, year = 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 }

Paul, Subhabrata; Pradhan, Dinabandhu; Verma, Shaily Vertex-edge domination in interval and bipartite permutation graphsDiscuss. Math. Graph Theory 2023: 947–963
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Given a graph \(G = (V,E)\), a vertex \(u \in V\) ve-dominates all edges incident to any vertex of \(N_G[u]\). A set \(D \subseteq V\) is a vertex-edge dominating set if for any edge \(e \in E\), there exists a vertex \(u \in D\) such that \(u\) ve-dominates \(e\). Given a graph \(G\), our goal is to find a minimum cardinality ve-dominating set of \(G\). In this paper, we designed two linear time algorithms to find a minimum cardinality ve-dominating set for interval and bipartite permutation graphs.
@article{DBLP:journals/dmgt/PaulPV23, abstract = {Given a graph \(G = (V,E)\), a vertex \(u \in V\) ve-dominates all edges incident to any vertex of \(N_G[u]\). A set \(D \subseteq V\) is a vertex-edge dominating set if for any edge \(e \in E\), there exists a vertex \(u \in D\) such that \(u\) ve-dominates \(e\). Given a graph \(G\), our goal is to find a minimum cardinality ve-dominating set of \(G\). In this paper, we designed two linear time algorithms to find a minimum cardinality ve-dominating set for interval and bipartite permutation graphs.}, author = {Paul, Subhabrata and Pradhan, Dinabandhu and Verma, Shaily}, journal = {Discuss. Math. Graph Theory}, keywords = {shailyverma dmgt year2023}, pages = {947&ndash;963}, title = {Vertex-edge domination in interval and bipartite permutation graphs}, year = 2023 }

Böther, Maximilian; Schiller, Leon; Fischbeck, Philipp; Molitor, Louise; Krejca, Martin S.; Friedrich, Tobias Evolutionary Minimization of Traffic CongestionIEEE Transactions on Evolutionary Computation 2023: 1809–1821
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
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 destination and 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 Berlin, Germany. We find that a combination of all operators yields the best result, reducing 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 et al. (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.
@article{2023evolutionary, 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 destination and 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 Berlin, Germany. We find that a combination of all operators yields the best result, reducing 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 et al. (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}, journal = {IEEE Transactions on Evolutionary Computation}, keywords = {maximilianboether philippfischbeck louisemolitor martinskrejca tobiasfriedrich tevoc leonschiller year2023}, number = 6, pages = {1809-1821}, title = {Evolutionary Minimization of Traffic Congestion}, volume = 27, year = 2023 }

Behrendt, Lukas; Casel, Katrin; Friedrich, Tobias; Lagodzinski, J. A. Gregor; Löser, Alexander; Wilhelm, Marcus From symmetry to asymmetry: Generalizing TSP approximations by parametrizationJournal of Computer and System Sciences 2023: 157–170
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
We generalize the tree doubling and Christofides algorithm to parameterized approximations for ATSP (constant factor approximations that invest more runtime with respect to a chosen parameter). The parameters we consider are upper bounded by the number of asymmetric distances, which yields algorithms to efficiently compute good approximations for moderately asymmetric TSP instances. As generalization of the Christofides algorithm, we derive a parameterized 2.5-approximation, with the size of a vertex cover for the subgraph induced by the edges with asymmetric distances as parameter. Our generalization of tree doubling 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 parameters we consider are theoretically incomparable, we present experimental results showing that generalized tree doubling frequently outperforms generalized Christofides with respect to parameter size.
@article{behrendt2023symmetry, abstract = {We generalize the tree doubling and Christofides algorithm to parameterized approximations for ATSP (constant factor approximations that invest more runtime with respect to a chosen parameter). The parameters we consider are upper bounded by the number of asymmetric distances, which yields algorithms to efficiently compute good approximations for moderately asymmetric TSP instances. As generalization of the Christofides algorithm, we derive a parameterized 2.5-approximation, with the size of a vertex cover for the subgraph induced by the edges with asymmetric distances as parameter. Our generalization of tree doubling 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 parameters we consider are theoretically incomparable, we present experimental results showing 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}, journal = {Journal of Computer and System Sciences}, keywords = {gregorlagodzinski alexanderloeser lukasbehrend katrincasel jcss tobiasfriedrich year2023 marcuswilhelm}, pages = {157-170}, title = {From symmetry to asymmetry: Generalizing TSP approximations by parametrization}, volume = 136, year = 2023 }

Krämer, Bastian; Stang, Moritz; Doskoč, Vanja; Schäfers, Wolfgang; Friedrich, Tobias Automated valuation models: improving model performance by choosing the optimal spatial training levelJournal of Property Research 2023: 365–390
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
The academic community has discussed using Automated Valuation Models (AVMs) in the context of traditional real estate valuations and their performance for several decades. Most studies focus on finding the best method for estimating property values. One aspect that has not yet to be studied scientifically is the appropriate choice of the spatial training level. The published research on AVMs usually deals with a manually defined region and fails to test the methods used on different spatial levels. Our research aims to investigate the impact of training AVM algorithms at different spatial levels regarding valuation accuracy. We use a dataset with 1.2 million residential properties from Germany and test four methods: Ordinary Least Square, Generalised Additive Models, eXtreme Gradient Boosting and Deep Neural Network. Our results show that the right choice of spatial training level can significantly impact the model performance, and that this impact varies across the different methods.
@article{kramer2023automated, abstract = {The academic community has discussed using Automated Valuation Models (AVMs) in the context of traditional real estate valuations and their performance for several decades. Most studies focus on finding the best method for estimating property values. One aspect that has not yet to be studied scientifically is the appropriate choice of the spatial training level. The published research on AVMs usually deals with a manually defined region and fails to test the methods used on different spatial levels. Our research aims to investigate the impact of training AVM algorithms at different spatial levels regarding valuation accuracy. We use a dataset with 1.2 million residential properties from Germany and test four methods: Ordinary Least Square, Generalised Additive Models, eXtreme Gradient Boosting and Deep Neural Network. Our results show that the right choice of spatial training level can significantly impact the model performance, and that this impact varies across the different methods.}, author = {Krämer, Bastian and Stang, Moritz and Doskoč, Vanja and Schäfers, Wolfgang and Friedrich, Tobias}, journal = {Journal of Property Research}, keywords = {sys:relevantfor:ae vanjadoskoc tobiasfriedrich year2023}, pages = {365-390}, title = {Automated valuation models: improving model performance by choosing the optimal spatial training level}, year = 2023 }

Cohen, Sarel; Hershcovitch, Moshik; Taraz, Martin; Kißig, Otto; Issac, Davis; Wood, Andrew; Waddington, Daniel; Chin, Peter; Friedrich, Tobias Improved And Optimized Drug Repurposing For The SARS-CoV-2 PandemicPlos One 2023
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
The active global SARS-CoV-2 pandemic caused more than 426 million cases and 5.8 million deaths worldwide. The development of completely new drugs for such a novel disease is a challenging, time intensive process. 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 8,070 candidate drugs, 32 of which are currently being tested 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.
@article{cohen2023improved, abstract = {The active global SARS-CoV-2 pandemic caused more than 426 million cases and 5.8 million deaths worldwide. The development of completely new drugs for such a novel disease is a challenging, time intensive process. 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 8,070 candidate drugs, 32 of which are currently being tested 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 = {Cohen, Sarel and Hershcovitch, Moshik and Taraz, Martin and Kißig, Otto and Issac, Davis and Wood, Andrew and Waddington, Daniel and Chin, Peter and Friedrich, Tobias}, journal = {Plos One}, keywords = {sarelcohen tobiasfriedrich year2023}, title = {Improved And Optimized Drug Repurposing For The SARS-CoV-2 Pandemic}, year = 2023 }

Friedrich, Tobias; Göbel, Andreas; Krejca, Martin S.; Pappik, Marcus Polymer Dynamics via Cliques: New Conditions for ApproximationsTheoretical Computer Science 2023: 230–252
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ 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}, pages = {230-252}, title = {Polymer Dynamics via Cliques: New Conditions for Approximations}, volume = 942, year = 2023 }

Bläsius, Thomas; Fischbeck, Philipp; Friedrich, Tobias; Katzmann, Maximilian Solving Vertex Cover in Polynomial Time on Hyperbolic Random GraphsTheory of Computing Systems 2023: 28–51
[ 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-2023, 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 year2023 maximiliankatzmann tocs}, number = 1, pages = {28&ndash;51}, title = {Solving Vertex Cover in Polynomial Time on Hyperbolic Random Graphs}, volume = 67, year = 2023 }

Wagner, Markus; Kohlros, Erik; Quantmeyer, Gerome; Kotzing, Timo ELEA – Build your own Evolutionary Algorithm in your BrowserGenetic and Evolutionary Computation Conference (GECCO ’23) 2023
[ Abstract ] [ BibTeX ] [ Download ]
 
We provide an open source framework to experiment with evolutionary algorithms which we call Experimenting and Learning toolkit for Evolutionary Algorithms (ELEA). ELEA is browser-based and allows to assemble evolutionary algorithms using drag-and-drop, starting from a number of simple predesigned examples, making the startup costs for employing the toolkit minimal. The designed examples can be executed and collected data can be displayed graphically. Further features include export of algorithm designs and experimental results as well as multi-threading. With the very intuitive user interface and the short time to get initial experiments going, this tool is especially suitable for explorative analyses of algorithms as well as for the use in classrooms.
@conference{wagner2023build, abstract = {We provide an open source framework to experiment with evolutionary algorithms which we call Experimenting and Learning toolkit for Evolutionary Algorithms (ELEA). ELEA is browser-based and allows to assemble evolutionary algorithms using drag-and-drop, starting from a number of simple predesigned examples, making the startup costs for employing the toolkit minimal. The designed examples can be executed and collected data can be displayed graphically. Further features include export of algorithm designs and experimental results as well as multi-threading. With the very intuitive user interface and the short time to get initial experiments going, this tool is especially suitable for explorative analyses of algorithms as well as for the use in classrooms.}, author = {Wagner, Markus and Kohlros, Erik and Quantmeyer, Gerome and Kotzing, Timo}, booktitle = {Genetic and Evolutionary Computation Conference (GECCO '23)}, keywords = {sys:relevantfor:ae timokoetzing gecco year2023}, title = {ELEA – Build your own Evolutionary Algorithm in your Browser}, year = 2023 }

Friedrich, Tobias; Lenzner, Pascal; Molitor, Louise; Seifert, Lars Single-Peaked Jump Schelling GamesInternational Symposium on Algorithmic Game Theory (SAGT) 2023
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Schelling games model the wide-spread phenomenon of residential segregation in metropolitan areas from a game-theoretic point of view. In these games agents of different types each strategically select a node on a given graph that models the residential area to maximize their individual utility. The latter solely depends on the types of the agents on neighboring nodes and it has been a standard assumption to consider utility functions that are monotone in the number of same-type neighbors. This simplifying assumption has recently been challenged since sociological poll results suggest that real-world agents actually favor diverse neighborhoods. We contribute to the recent endeavor of investigating residential segregation models with realistic agent behavior by studying Jump Schelling Games with agents having a single-peaked utility function. In such games, there are empty nodes in the graph and agents can strategically jump to such nodes to improve their utility. We investigate the existence of equilibria and show that they exist under specific conditions. Contrasting this, we prove that even on simple topologies like paths or rings such stable states are not guaranteed to exist. Regarding the game dynamics, we show that improving response cycles exist independently of the position of the peak in the utility function. Moreover, we show high almost tight bounds on the Price of Anarchy and the Price of Stability with respect to the recently proposed degree of integration, which counts the number of agents with a diverse neighborhood and which serves as a proxy for measuring the segregation strength. Last but not least, we show that computing a beneficial state with high integration is NP-complete and, as a novel conceptual contribution, we also show that it is NP-hard to decide if an equilibrium state can be found via improving response dynamics starting from a given initial state.
@inproceedings{friedrich2023singlepeaked, abstract = {Schelling games model the wide-spread phenomenon of residential segregation in metropolitan areas from a game-theoretic point of view. In these games agents of different types each strategically select a node on a given graph that models the residential area to maximize their individual utility. The latter solely depends on the types of the agents on neighboring nodes and it has been a standard assumption to consider utility functions that are monotone in the number of same-type neighbors. This simplifying assumption has recently been challenged since sociological poll results suggest that real-world agents actually favor diverse neighborhoods. We contribute to the recent endeavor of investigating residential segregation models with realistic agent behavior by studying Jump Schelling Games with agents having a single-peaked utility function. In such games, there are empty nodes in the graph and agents can strategically jump to such nodes to improve their utility. We investigate the existence of equilibria and show that they exist under specific conditions. Contrasting this, we prove that even on simple topologies like paths or rings such stable states are not guaranteed to exist. Regarding the game dynamics, we show that improving response cycles exist independently of the position of the peak in the utility function. Moreover, we show high almost tight bounds on the Price of Anarchy and the Price of Stability with respect to the recently proposed degree of integration, which counts the number of agents with a diverse neighborhood and which serves as a proxy for measuring the segregation strength. Last but not least, we show that computing a beneficial state with high integration is NP-complete and, as a novel conceptual contribution, we also show that it is NP-hard to decide if an equilibrium state can be found via improving response dynamics starting from a given initial state.}, author = {Friedrich, Tobias and Lenzner, Pascal and Molitor, Louise and Seifert, Lars}, journal = {International Symposium on Algorithmic Game Theory (SAGT)}, keywords = {louisemolitor tobiasfriedrich year2023 larsseifert pascallenzner sagt}, title = {Single-Peaked Jump Schelling Games}, year = 2023 }

Quinzan, Francesco; Khanna, Rajiv; Hershcovitch, Moshik; Cohen, Sarel; Waddington, Daniel G.; Friedrich, Tobias; Mahoney, Michael W. Fast Feature Selection with Fairness ConstraintsArtificial Intelligence and Statistics (AISTATS) 2023: 7800–7823
[ Abstract ] [ BibTeX ] [ URL ] [ Download ]
 
We study the fundamental problem of selecting optimal features for model construction. This problem is computationally challenging on large datasets, even with the use of greedy algorithm variants. To address this challenge, we extend the adaptive query model, recently proposed for the greedy forward selection for submodular functions, to the faster paradigm of Orthogonal Matching Pursuit for non-submodular functions. The proposed algorithm achieves exponentially fast parallel run time in the adaptive query model, scaling much better than prior work. Furthermore, our extension allows the use of downward-closed constraints, which can be used to encode certain fairness criteria into the feature selection process. We prove strong approximation guarantees for the algorithm based on standard assumptions. These guarantees are applicable to many parametric models, including Generalized Linear Models. Finally, we demonstrate empirically that the proposed algorithm competes favorably with state-of-the-art techniques for feature selection, on real-world and synthetic datasets.
@inproceedings{quinzan2023feature, abstract = {We study the fundamental problem of selecting optimal features for model construction. This problem is computationally challenging on large datasets, even with the use of greedy algorithm variants. To address this challenge, we extend the adaptive query model, recently proposed for the greedy forward selection for submodular functions, to the faster paradigm of Orthogonal Matching Pursuit for non-submodular functions. The proposed algorithm achieves exponentially fast parallel run time in the adaptive query model, scaling much better than prior work. Furthermore, our extension allows the use of downward-closed constraints, which can be used to encode certain fairness criteria into the feature selection process. We prove strong approximation guarantees for the algorithm based on standard assumptions. These guarantees are applicable to many parametric models, including Generalized Linear Models. Finally, we demonstrate empirically that the proposed algorithm competes favorably with state-of-the-art techniques for feature selection, on real-world and synthetic datasets.}, author = {Quinzan, Francesco and Khanna, Rajiv and Hershcovitch, Moshik and Cohen, Sarel and Waddington, Daniel G. and Friedrich, Tobias and Mahoney, Michael W.}, journal = {Artificial Intelligence and Statistics (AISTATS)}, keywords = {sarelcohen aistats francescoquinzan tobiasfriedrich year2023}, pages = {7800&ndash;7823}, title = {Fast Feature Selection with Fairness Constraints}, year = 2023 }

Krogmann, Simon; Lenzner, Pascal; Skopalik, Alexander Strategic Facility Location with Clients that Minimize Total Waiting TimeConference on Artificial Intelligence (AAAI) 2023: 5714–5721
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
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}, number = 5, pages = {5714-5721}, title = {Strategic Facility Location with Clients that Minimize Total Waiting Time}, volume = 37, year = 2023 }

Blažej, Václav; Ganian, Robert; Knop, Dušan; Pokorný, Jan; Schierreich, Šimon; Simonov, Kirill The Parameterized Complexity of Network MicroaggregationConference on Artificial Intelligence (AAAI) 2023: 6262–6270
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Microaggregation is a classical statistical disclosure control technique which requires the input data to be partitioned into clusters while adhering to specified size constraints. We provide novel exact algorithms and lower bounds for the task of microaggregating a given network while considering both unrestricted and connected clusterings, and analyze these from the perspective of the parameterized complexity paradigm. Altogether, our results assemble a complete complexity-theoretic picture for the network microaggregation problem with respect to the most natural parameteri- zations of the problem, including input-specified parameters capturing the size and homogeneity of the clusters as well as the treewidth and vertex cover number of the network.
@inproceedings{blazej2023parameterized, abstract = {Microaggregation is a classical statistical disclosure control technique which requires the input data to be partitioned into clusters while adhering to specified size constraints. We provide novel exact algorithms and lower bounds for the task of microaggregating a given network while considering both unrestricted and connected clusterings, and analyze these from the perspective of the parameterized complexity paradigm. Altogether, our results assemble a complete complexity-theoretic picture for the network microaggregation problem with respect to the most natural parameteri- zations of the problem, including input-specified parameters capturing the size and homogeneity of the clusters as well as the treewidth and vertex cover number of the network.}, author = {Blažej, Václav and Ganian, Robert and Knop, Dušan and Pokorný, Jan and Schierreich, Šimon and Simonov, Kirill}, booktitle = {Conference on Artificial Intelligence (AAAI)}, keywords = {sys:relevantfor:ae kirillsimonov aaai year2023}, pages = {6262&ndash;6270}, title = {The Parameterized Complexity of Network Microaggregation}, year = 2023 }

Brand, Cornelius; Ganian, Robert; Simonov, Kirill A Parameterized Theory of PAC LearningConference on Artificial Intelligence (AAAI) 2023: 6834–6841
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Probably Approximately Correct (i.e., PAC) learning is a core concept of sample complexity theory, and efficient PAC learnability is often seen as a natural counterpart to the class P in classical computational complexity. But while the nascent theory of parameterized complexity has allowed us to push beyond the P-NP “dichotomy” in classical computational complexity and identify the exact boundaries of tractability for numerous problems, there is no analogue in the domain of sample complexity that could push beyond efficient PAC learnability. As our core contribution, we fill this gap by developing a theory of parameterized PAC learning which allows us to shed new light on several recent PAC learning results that incorporated elements of parameterized complexity. Within the theory, we identify not one but two notions of fixed-parameter learnability that both form distinct counterparts to the class FPT—the core concept at the center of the parameterized complexity paradigm—and develop the machinery required to exclude fixed-parameter learnability. We then showcase the applications of this theory to identify refined boundaries of tractability for CNF and DNF learning as well as for a range of learning problems on graphs.
@inproceedings{brand2023parameterized, abstract = {Probably Approximately Correct (i.e., PAC) learning is a core concept of sample complexity theory, and efficient PAC learnability is often seen as a natural counterpart to the class P in classical computational complexity. But while the nascent theory of parameterized complexity has allowed us to push beyond the P-NP “dichotomy” in classical computational complexity and identify the exact boundaries of tractability for numerous problems, there is no analogue in the domain of sample complexity that could push beyond efficient PAC learnability. As our core contribution, we fill this gap by developing a theory of parameterized PAC learning which allows us to shed new light on several recent PAC learning results that incorporated elements of parameterized complexity. Within the theory, we identify not one but two notions of fixed-parameter learnability that both form distinct counterparts to the class FPT—the core concept at the center of the parameterized complexity paradigm—and develop the machinery required to exclude fixed-parameter learnability. We then showcase the applications of this theory to identify refined boundaries of tractability for CNF and DNF learning as well as for a range of learning problems on graphs.}, author = {Brand, Cornelius and Ganian, Robert and Simonov, Kirill}, booktitle = {Conference on Artificial Intelligence (AAAI)}, keywords = {sys:relevantfor:ae kirillsimonov aaai year2023}, pages = {6834&ndash;6841}, title = {A Parameterized Theory of PAC Learning}, year = 2023 }

Cseh, Ágnes; Führlich, Pascal; Lenzner, Pascal The Swiss GambitAutonomous Agents and Multi-Agent Systems (AAMAS) 2023
[ Abstract ] [ BibTeX ] [ URL ] [ Download ]
 
In each round of a Swiss-system tournament, players of similar score are paired against each other. An intentional early loss therefore might lead to weaker opponents in later rounds and thus to a better final tournament result a phenomenon known as the Swiss Gambit. To the best of our knowledge it is an open question whether this strategy can actually work. This paper provides answers based on an empirical agent-based analysis for the most prominent application area of the Swiss-system format, namely chess tournaments. We simulate realistic tournaments by employing the official FIDE pairing system for computing the player pairings in each round. We show that even though gambits are widely possible in Swiss-system chess tournaments, profiting from them requires a high degree of predictability of match results. Moreover, even if a Swiss Gambit succeeds, the obtained improvement in the final ranking is limited. Our experiments prove that counting on a Swiss Gambit is indeed a lot more of a risky gambit than a reliable strategy to improve the final rank.
@inproceedings{cseh2023swiss, abstract = {In each round of a Swiss-system tournament, players of similar score are paired against each other. An intentional early loss therefore might lead to weaker opponents in later rounds and thus to a better final tournament result a phenomenon known as the Swiss Gambit. To the best of our knowledge it is an open question whether this strategy can actually work. This paper provides answers based on an empirical agent-based analysis for the most prominent application area of the Swiss-system format, namely chess tournaments. We simulate realistic tournaments by employing the official FIDE pairing system for computing the player pairings in each round. We show that even though gambits are widely possible in Swiss-system chess tournaments, profiting from them requires a high degree of predictability of match results. Moreover, even if a Swiss Gambit succeeds, the obtained improvement in the final ranking is limited. Our experiments prove that counting on a Swiss Gambit is indeed a lot more of a risky gambit than a reliable strategy to improve the final rank.}, author = {Cseh, Ágnes and Führlich, Pascal and Lenzner, Pascal}, booktitle = {Autonomous Agents and Multi-Agent Systems (AAMAS)}, keywords = {agnescseh aamas year2023 pascallenzner}, title = {The Swiss Gambit}, year = 2023 }

Bertschinger, Nils; Hoefer, Martin; Krogmann, Simon; Lenzner, Pascal; Schuldenzucker, Steffen; Wilhelmi, Lisa Equilibria and Convergence in Fire Sale GamesAutonomous Agents and Multiagent Systems (AAMAS) 2023: 215–223
[ Abstract ] [ BibTeX ] [ URL ] [ Download ]
 
The complex interactions between algorithmic trading agents can have a severe influence on the functioning of our economy, as witnessed by recent banking crises and trading anomalies. A common phenomenon in these situations are fire sales, a contagious process of asset sales that trigger further sales. We study the existence and structure of equilibria in a game-theoretic model of fire sales. We prove that for a wide parameter range (e.g., convex price impact functions), equilibria exist and form a complete lattice. This is contrasted with a non-existence result for concave price impact functions. Moreover, we study the convergence of best-response dynamics towards equilibria when they exist. In general, best-response dynamics may cycle. However, in many settings they are guaranteed to converge to the socially optimal equilibrium when starting from a natural initial state. Moreover, we discuss a simplified variant of the dynamics that is less informationally demanding and converges to the same equilibria. We compare the dynamics in terms of convergence speed.
@inproceedings{bertschinger2023equilibria, abstract = {The complex interactions between algorithmic trading agents can have a severe influence on the functioning of our economy, as witnessed by recent banking crises and trading anomalies. A common phenomenon in these situations are fire sales, a contagious process of asset sales that trigger further sales. We study the existence and structure of equilibria in a game-theoretic model of fire sales. We prove that for a wide parameter range (e.g., convex price impact functions), equilibria exist and form a complete lattice. This is contrasted with a non-existence result for concave price impact functions. Moreover, we study the convergence of best-response dynamics towards equilibria when they exist. In general, best-response dynamics may cycle. However, in many settings they are guaranteed to converge to the socially optimal equilibrium when starting from a natural initial state. Moreover, we discuss a simplified variant of the dynamics that is less informationally demanding and converges to the same equilibria. We compare the dynamics in terms of convergence speed.}, author = {Bertschinger, Nils and Hoefer, Martin and Krogmann, Simon and Lenzner, Pascal and Schuldenzucker, Steffen and Wilhelmi, Lisa}, booktitle = {Autonomous Agents and Multiagent Systems (AAMAS)}, keywords = {aamas year2023 simonkrogmann pascallenzner}, pages = {215-223}, title = {Equilibria and Convergence in Fire Sale Games}, year = 2023 }

Doering, Michelle; Peters, Jannik Margin of Victory for Weighted Tournament SolutionsAutonomous Agents and Multi-Agent Systems (AAMAS) 2023: 1716–1724
[ Abstract ] [ BibTeX ] [ URL ] [ Download ]
 
Determining how close a winner of an election is to becoming a loser, or distinguishing between different possible winners of an election, are major problems in computational social choice. We tackle these problems for so-called weighted tournament solutions by generalizing the notion of margin of victory (MoV) for tournament solutions by Brill et al. [2022][Artificial Intelligence] to weighted tournament solutions. For these, the MoV of a winner (resp. loser) is the total weight that needs to be changed in the tournament to make them a loser (resp. winner). We study three weighted tournament solutions: Borda’s rule, the weighted Uncovered Set, and Split Cycle. For all three rules, we determine whether the MoV for winners and non-winners is tractable and give upper and lower bounds on the possible values of the MoV. Further, we axiomatically study and generalize properties from the unweighted tournament setting to weighted tournaments.
@inproceedings{doering2023margin, abstract = {Determining how close a winner of an election is to becoming a loser, or distinguishing between different possible winners of an election, are major problems in computational social choice. We tackle these problems for so-called weighted tournament solutions by generalizing the notion of margin of victory (MoV) for tournament solutions by Brill et al. [2022][Artificial Intelligence] to weighted tournament solutions. For these, the MoV of a winner (resp. loser) is the total weight that needs to be changed in the tournament to make them a loser (resp. winner). We study three weighted tournament solutions: Borda’s rule, the weighted Uncovered Set, and Split Cycle. For all three rules, we determine whether the MoV for winners and non-winners is tractable and give upper and lower bounds on the possible values of the MoV. Further, we axiomatically study and generalize properties from the unweighted tournament setting to weighted tournaments.}, author = {Doering, Michelle and Peters, Jannik}, booktitle = {Autonomous Agents and Multi-Agent Systems (AAMAS)}, keywords = {aamas year2023 michelledoering}, pages = {1716&ndash;1724}, title = {Margin of Victory for Weighted Tournament Solutions}, year = 2023 }

Deligkas, Argyrios; Eiben, Eduard; Goldsmith, Tiger-Lily; Skretas, George Being an Influencer is Hard: The Complexity of Influence Maximization in Temporal Graphs with a Fixed SourceAutonomous Agents and Multi-Agent Systems (AAMAS) 2023: 2222–2230
[ Abstract ] [ BibTeX ] [ URL ] [ Download ]
 
We consider the influence maximization problem over a temporal graph, where there is a single fixed source. We deviate from the standard model of influence maximization, where the goal is to choose the set of most influential vertices. Instead, in our model we are given a fixed vertex, or source, and the goal is to find the best time steps to transmit so that the influence of this vertex is maximized. We frame this problem as a spreading process that follows a variant of the susceptible-infected-susceptible (SIS) model and we focus on three objective functions.In the MaxSpread objective, the goal is to maximize the total number of vertices that get infected at least once. In the MaxViral objective, the goal is to maximize the number of vertices that are infected at the same time step. Finally, in MaxViralTstep, the goal is to maximize the number of vertices that are infected at a given time step. We perform a thorough complexity theoretic analysis for these three objectives over three different scenarios: (1) the unconstrained setting where the source can transmit whenever it wants; (2) the window-constrained setting where the source has to transmit at either a predetermined, or a shifting window; (3) the periodic setting where the temporal graph has a small period. We prove that all of these problems, with the exception of MaxSpread for periodic graphs, are intractable even for very simple underlying graphs.
@inproceedings{deligkas2023being, abstract = {We consider the influence maximization problem over a temporal graph, where there is a single fixed source. We deviate from the standard model of influence maximization, where the goal is to choose the set of most influential vertices. Instead, in our model we are given a fixed vertex, or source, and the goal is to find the best time steps to transmit so that the influence of this vertex is maximized. We frame this problem as a spreading process that follows a variant of the susceptible-infected-susceptible (SIS) model and we focus on three objective functions.In the MaxSpread objective, the goal is to maximize the total number of vertices that get infected at least once. In the MaxViral objective, the goal is to maximize the number of vertices that are infected at the same time step. Finally, in MaxViralTstep, the goal is to maximize the number of vertices that are infected at a given time step. We perform a thorough complexity theoretic analysis for these three objectives over three different scenarios: (1) the unconstrained setting where the source can transmit whenever it wants; (2) the window-constrained setting where the source has to transmit at either a predetermined, or a shifting window; (3) the periodic setting where the temporal graph has a small period. We prove that all of these problems, with the exception of MaxSpread for periodic graphs, are intractable even for very simple underlying graphs.}, author = {Deligkas, Argyrios and Eiben, Eduard and Goldsmith, Tiger-Lily and Skretas, George}, booktitle = {Autonomous Agents and Multi-Agent Systems (AAMAS)}, keywords = {sys:relevantfor:ae aamas year2023 michelledoering georgeskretas}, pages = {2222&ndash;2230}, title = {Being an Influencer is Hard: The Complexity of Influence Maximization in Temporal Graphs with a Fixed Source}, year = 2023 }

Friedrich, Tobias; Lenzner, Pascal; Molitor, Louise; Seifert, Lars Single-Peaked Jump Schelling GamesAutonomous Agents and Multiagent Systems (AAMAS) 2023: 2899–2901
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Schelling games model the wide-spread phenomenon of residential segregation in metropolitan areas from a game-theoretic point of view. In these games agents of different types each strategically select a node on a given graph that models the residential area to maximize their individual utility. The latter solely depends on the types of the agents on neighboring nodes and it has been a standard assumption to consider utility functions that are monotone in the number of same-type neighbors. This simplifying assumption has recently been challenged since sociological poll results suggest that real-world agents actually favor diverse neighborhoods. We contribute to the recent endeavor of investigating residential segregation models with realistic agent behavior by studying Jump Schelling Games with agents having a single-peaked utility function. In such games, there are empty nodes in the graph and agents can strategically jump to such nodes to improve their utility. We investigate the existence of equilibria and show that they exist under specific conditions. Contrasting this, we prove that even on simple topologies like paths or rings such stable states are not guaranteed to exist. Regarding the game dynamics, we show that improving response cycles exist independently of the position of the peak in the utility function. Moreover, we show high almost tight bounds on the Price of Anarchy and the Price of Stability with respect to the recently proposed degree of integration, which counts the number of agents with a diverse neighborhood and which serves as a proxy for measuring the segregation strength. Last but not least, we show that computing a beneficial state with high integration is NP-complete and, as a novel conceptual contribution, we also show that it is NP-hard to decide if an equilibrium state can be found via improving response dynamics starting from a given initial state.
@inproceedings{friedrich2023singlepeaked, abstract = {Schelling games model the wide-spread phenomenon of residential segregation in metropolitan areas from a game-theoretic point of view. In these games agents of different types each strategically select a node on a given graph that models the residential area to maximize their individual utility. The latter solely depends on the types of the agents on neighboring nodes and it has been a standard assumption to consider utility functions that are monotone in the number of same-type neighbors. This simplifying assumption has recently been challenged since sociological poll results suggest that real-world agents actually favor diverse neighborhoods. We contribute to the recent endeavor of investigating residential segregation models with realistic agent behavior by studying Jump Schelling Games with agents having a single-peaked utility function. In such games, there are empty nodes in the graph and agents can strategically jump to such nodes to improve their utility. We investigate the existence of equilibria and show that they exist under specific conditions. Contrasting this, we prove that even on simple topologies like paths or rings such stable states are not guaranteed to exist. Regarding the game dynamics, we show that improving response cycles exist independently of the position of the peak in the utility function. Moreover, we show high almost tight bounds on the Price of Anarchy and the Price of Stability with respect to the recently proposed degree of integration, which counts the number of agents with a diverse neighborhood and which serves as a proxy for measuring the segregation strength. Last but not least, we show that computing a beneficial state with high integration is NP-complete and, as a novel conceptual contribution, we also show that it is NP-hard to decide if an equilibrium state can be found via improving response dynamics starting from a given initial state.}, author = {Friedrich, Tobias and Lenzner, Pascal and Molitor, Louise and Seifert, Lars}, booktitle = {Autonomous Agents and Multiagent Systems (AAMAS)}, keywords = {louisemolitor tobiasfriedrich aamas year2023 larsseifert pascallenzner}, pages = {2899&ndash;2901}, title = {Single-Peaked Jump Schelling Games}, year = 2023 }

Becher, Kilian; Lagodzinski, J. A. Gregor; Parra-Arnau, Javier; Strufe, Thorsten Analysis and Prevention of Averaging Attacks Against Obfuscation ProtocolsApplied Cryptography and Network Security (ACNS), Part I 2023: 451–475
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Verification and traceability of supply-chain data is a common example for public analysis of confidential data. Finding the correct balance between confidentiality and utility often is anything but trivial. In order to ensure confidentiality and thus protect companies’ competitive advantages, existing approaches employ probabilistic output obfuscation. However, it is known that this form of obfuscation might render a system subject to averaging attacks. In these attacks, an adversary repeatedly queries for the same analysis and combines the probabilistic outputs, thus implementing an estimator that eliminates the obfuscation. A clear picture on the performance of such attacks is missing, information that is crucial for mitigating averaging attacks. Our contributions are threefold: First, using an existing supply-chain verification protocol (RVP) as a particularly efficient example of protocols with output obfuscation, we extensively analyze the risk posed by averaging attacks. We prove rigorously that such attacks perform exceptionally well if obfuscation is based on random values sampled independently in every query. We generalize our analysis to all protocols that employ probabilistic output obfuscation. Second, we propose the paradigm of data-dependent deterministic obfuscation (D3O) to prevent such attacks. Third, we present mRVP, a D3O-based version of RVP, and empirically demonstrate practicality and effectiveness of D3O. The results show that our mitigations add negligible runtime overhead, do not affect accuracy, and effectively retain confidentiality.
@inproceedings{becher2023analysis, abstract = {Verification and traceability of supply-chain data is a common example for public analysis of confidential data. Finding the correct balance between confidentiality and utility often is anything but trivial. In order to ensure confidentiality and thus protect companies’ competitive advantages, existing approaches employ probabilistic output obfuscation. However, it is known that this form of obfuscation might render a system subject to averaging attacks. In these attacks, an adversary repeatedly queries for the same analysis and combines the probabilistic outputs, thus implementing an estimator that eliminates the obfuscation. A clear picture on the performance of such attacks is missing, information that is crucial for mitigating averaging attacks. Our contributions are threefold: First, using an existing supply-chain verification protocol (RVP) as a particularly efficient example of protocols with output obfuscation, we extensively analyze the risk posed by averaging attacks. We prove rigorously that such attacks perform exceptionally well if obfuscation is based on random values sampled independently in every query. We generalize our analysis to all protocols that employ probabilistic output obfuscation. Second, we propose the paradigm of data-dependent deterministic obfuscation (D3O) to prevent such attacks. Third, we present mRVP, a D3O-based version of RVP, and empirically demonstrate practicality and effectiveness of D3O. The results show that our mitigations add negligible runtime overhead, do not affect accuracy, and effectively retain confidentiality.}, author = {Becher, Kilian and Lagodzinski, J. A. Gregor and Parra-Arnau, Javier and Strufe, Thorsten}, booktitle = {Applied Cryptography and Network Security (ACNS), Part {I}}, editor = {Tibouchi, Mehdi and Wang, Xiaofeng}, keywords = {gregorlagodzinski thorstenstrufe acns javierparra-arnau year2023 kilianbecher}, pages = {451&ndash;475}, publisher = {Springer}, title = {Analysis and Prevention of Averaging Attacks Against Obfuscation Protocols}, volume = 13905, year = 2023 }

Böther, Maximilian; Kißig, Otto; Weyand, Christopher Efficiently Computing Directed Minimum Spanning TreesSIAM Symposium on Algorithm Engineering and Experiments (ALENEX) 2023: 86–95
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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}, pages = {86&ndash;95}, title = {Efficiently Computing Directed Minimum Spanning Trees}, year = 2023 }

Khomutovskiy, Ivan; Dunker, Rebekka; Dierking, Jessica; Egbert, Julian; Helms, Christian; Schöllkopf, Finn; Casel, Katrin; Fischbeck, Philipp; Friedrich, Tobias; Isaac, Davis; Krogmann, Simon; Lenzner, Pascal Applying Skeletons to Speed Up the Arc-Flags Routing AlgorithmSIAM Symposium on Algorithm Engineering and Experiments (ALENEX) 2023: 110–122
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
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 = {Khomutovskiy, Ivan and Dunker, Rebekka and Dierking, Jessica and Egbert, Julian and Helms, Christian and Schöllkopf, Finn and Casel, Katrin and Fischbeck, Philipp and Friedrich, Tobias and Isaac, Davis and Krogmann, Simon and Lenzner, Pascal}, booktitle = {SIAM Symposium on Algorithm Engineering and Experiments (ALENEX)}, keywords = {alenex philippfischbeck katrincasel davisissac tobiasfriedrich year2023 simonkrogmann pascallenzner}, pages = {110-122}, title = {Applying Skeletons to Speed Up the Arc-Flags Routing Algorithm}, year = 2023 }

Krämer, Bastian; Stang, Moritz; Doskoč, Vanja; Schäfers, Wolfgang; Friedrich, Tobias Automated Valuation Models: Improving Model Performance by Choosing the Optimal Spatial Training LevelAmerican Real Estate Society (ARES) 2023: 1–26
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
The use of Automated Valuation Models (AVMs) in the context of traditional real estate valuations and their performance has been discussed in the academic community for several decades. Most studies focus on finding which method is best suited for estimating property values. One aspect that has not yet been studied scientifically is the appropriate choice of the spatial training level. The published research on AVMs usually deals with a manually defined region and fails to test the methods used on different spatial levels. The aim of our research is thus to investigate the impact of training AVM algorithms at different spatial levels in terms of valuation accuracy. We use a dataset with about 1.2 million residential properties from Germany and test four different methods, namely Ordinary Least Square, Generalized Additive Models, eXtreme Gradient Boosting and Deep Neural Network. Our results show that the right choice of spatial training level can have a major impact on the model performance, and that this impact varies across the different methods.
@inproceedings{kramer2023automated, abstract = {The use of Automated Valuation Models (AVMs) in the context of traditional real estate valuations and their performance has been discussed in the academic community for several decades. Most studies focus on finding which method is best suited for estimating property values. One aspect that has not yet been studied scientifically is the appropriate choice of the spatial training level. The published research on AVMs usually deals with a manually defined region and fails to test the methods used on different spatial levels. The aim of our research is thus to investigate the impact of training AVM algorithms at different spatial levels in terms of valuation accuracy. We use a dataset with about 1.2 million residential properties from Germany and test four different methods, namely Ordinary Least Square, Generalized Additive Models, eXtreme Gradient Boosting and Deep Neural Network. Our results show that the right choice of spatial training level can have a major impact on the model performance, and that this impact varies across the different methods.}, author = {Krämer, Bastian and Stang, Moritz and Doskoč, Vanja and Schäfers, Wolfgang and Friedrich, Tobias}, booktitle = {American Real Estate Society (ARES)}, keywords = {moritzstang ares vanjadoskoc tobiasfriedrich wolfgangschaefers bastiankraemer year2023}, pages = {1-26}, title = {Automated Valuation Models: Improving Model Performance by Choosing the Optimal Spatial Training Level}, year = 2023 }

Jana, Satyabrata; Saha, Souvik; Sahu, Abhishek; Saurabh, Saket; Verma, Shaily Partitioning Subclasses of Chordal Graphs with Few DeletionsConference on Algorithms and Complexity (CIAC) 2023: 293–307
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In the (Vertex) \(k\)-Way Cut problem, input is an undirected graph \(G\), an integer \(s\), and the goal is to find a subset \(S\) of edges (vertices) of size at most \(s\), such that \(G-S\) has at least \(k\) connected components. Downey et al. [Electr. Notes Theor. Comput. Sci. 2003] showed that \(k\)-Way Cut is W[1]-hard parameterized by \( k \). However, Kawarabayashi and Throup [FOCS 2011] showed that the problem is fixed-parameter tractable (FPT) in general graphs with respect to the parameter \(s\) and provided a \(\mathcal{O(s^s^\mathcal{O(s) n^2) \) time algorithm, where \(n \) denotes the number of vertices in \(G \). The best-known algorithm for this problem runs in time \(s^{\mathcal{O(s) n^\mathcal{O(1)}\) given by Lokshtanov et al. [ACM Tran. of Algo. 2021]. On the other hand, Vertex \(k\)-Way Cut is W[1]-hard with respect to either of the parameters, \(k\) or \(s\) or \(k+s\). These algorithmic results motivate us to look at the problems on special classes of graphs. In this paper, we consider the (Vertex) \(k\)-Way Cut problem on subclasses of chordal graphs and obtain the following results. (i) We first give a sub-exponential FPT algorithm for \(k\)-Way Cut running in time \(2^{\mathcal{O(\sqrt{s} \log s) n^\mathcal{O(1)}\) on chordal graphs. (ii) It is known that Vertex \(k\)-Way Cut is W[1]-hard on chordal graphs, in fact on split graphs, parameterized by \(k+s\). We complement this hardness result by designing polynomial-time algorithms for Vertex \(k\)-Way Cut on interval graphs, circular-arc graphs and permutation graphs.
@inproceedings{DBLP:conf/ciac/JanaSSSV23, abstract = {In the (Vertex) \(k\)-Way Cut problem, input is an undirected graph \(G\), an integer \(s\), and the goal is to find a subset \(S\) of edges (vertices) of size at most \(s\), such that \(G-S\) has at least \(k\) connected components. Downey et al. [Electr. Notes Theor. Comput. Sci. 2003] showed that \(k\)-Way Cut is W[1]-hard parameterized by \( k \). However, Kawarabayashi and Throup [FOCS 2011] showed that the problem is fixed-parameter tractable (FPT) in general graphs with respect to the parameter \(s\) and provided a \(\mathcal{O}(s^{s^{\mathcal{O}(s)}} n^2) \) time algorithm, where \(n \) denotes the number of vertices in \(G \). The best-known algorithm for this problem runs in time \(s^{\mathcal{O}(s)} n^{\mathcal{O}(1)}\) given by Lokshtanov et al. [ACM Tran. of Algo. 2021]. On the other hand, Vertex \(k\)-Way Cut is W[1]-hard with respect to either of the parameters, \(k\) or \(s\) or \(k+s\). These algorithmic results motivate us to look at the problems on special classes of graphs. In this paper, we consider the (Vertex) \(k\)-Way Cut problem on subclasses of chordal graphs and obtain the following results. (i) We first give a sub-exponential FPT algorithm for \(k\)-Way Cut running in time \(2^{\mathcal{O}(\sqrt{s} \log s)} n^{\mathcal{O}(1)}\) on chordal graphs. (ii) It is known that Vertex \(k\)-Way Cut is W[1]-hard on chordal graphs, in fact on split graphs, parameterized by \(k+s\). We complement this hardness result by designing polynomial-time algorithms for Vertex \(k\)-Way Cut on interval graphs, circular-arc graphs and permutation graphs.}, author = {Jana, Satyabrata and Saha, Souvik and Sahu, Abhishek and Saurabh, Saket and Verma, Shaily}, booktitle = {Conference on Algorithms and Complexity (CIAC)}, keywords = {ciac shailyverma year2023}, pages = {293&ndash;307}, title = {Partitioning Subclasses of Chordal Graphs with Few Deletions}, year = 2023 }

Bläsius, Thomas; Friedrich, Tobias; Katzmann, Maximilian; Ruff, Janosch; Zeif, Ziena On the Giant Component of Geometric Inhomogeneous Random GraphsEuropean Symposium on Algorithms (ESA) 2023: 20:1–20:13
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
In this paper we study the threshold model of geometric inhomogeneous random graphs (GIRGs); a generative random graph model that is closely related to hyperbolic random graphs (HRGs). These models have been observed to capture complex real-world networks well with respect to the structural and algorithmic properties. Following comprehensive studies regarding their connectivity, i.e., which parts of the graphs are connected, we have a good understanding under which circumstances a giant component (containing a constant fraction of the graph) emerges. While previous results are rather technical and challenging to work with, the goal of this paper is to provide more accessible proofs. At the same time we significantly improve the previously known probabilistic guarantees, showing that GIRGs contain a giant component with probability \( 1 - exp(-Omega (n^(3-\tau )/2})) \) for graph size \(n\) and a degree distribution with power-law exponent \(tau in (2, 3)\). Based on that we additionally derive insights about the connectivity of certain induced subgraphs of GIRGs.
@inproceedings{blasius2023giant, abstract = {In this paper we study the threshold model of geometric inhomogeneous random graphs (GIRGs); a generative random graph model that is closely related to hyperbolic random graphs (HRGs). These models have been observed to capture complex real-world networks well with respect to the structural and algorithmic properties. Following comprehensive studies regarding their connectivity, i.e., which parts of the graphs are connected, we have a good understanding under which circumstances a giant component (containing a constant fraction of the graph) emerges. While previous results are rather technical and challenging to work with, the goal of this paper is to provide more accessible proofs. At the same time we significantly improve the previously known probabilistic guarantees, showing that GIRGs contain a giant component with probability \( 1 - exp(-\Omega (n^{(3-\tau )/2})) \) for graph size \(n\) and a degree distribution with power-law exponent \(\tau \in (2, 3)\). Based on that we additionally derive insights about the connectivity of certain induced subgraphs of GIRGs.}, author = {Bläsius, Thomas and Friedrich, Tobias and Katzmann, Maximilian and Ruff, Janosch and Zeif, Ziena}, booktitle = {European Symposium on Algorithms (ESA)}, keywords = {zienazeif esa thomasblaesius janoschruff tobiasfriedrich year2023 maximiliankatzmann}, pages = {20:1&ndash;20:13}, title = {On the Giant Component of Geometric Inhomogeneous Random Graphs}, year = 2023 }

Casel, Katrin; Friedrich, Tobias; Schirneck, Martin; Wietheger, Simon Fair Correlation Clustering in ForestsFoundations of Responsible Computing (FORC) 2023: 9:1–9:12
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
The study of algorithmic fairness received growing attention recently. This stems from the awareness that bias in the input data for machine learning systems may result in discriminatory outputs. For clustering tasks, one of the most central notions of fairness is the formalization by Chierichetti, Kumar, Lattanzi, and Vassilvitskii [NeurIPS 2017]. A clustering is said to be fair, if each cluster has the same distribution of manifestations of a sensitive attribute as the whole input set. This is motivated by various applications where the objects to be clustered have sensitive attributes that should not be over- or underrepresented. Most research on this version of fair clustering has focused on centriod-based objectives. In contrast, we discuss the applicability of this fairness notion to Correlation Clustering. The existing literature on the resulting Fair Correlation Clustering problem either presents approximation algorithms with poor approximation guarantees or severely limits the possible distributions of the sensitive attribute (often only two manifestations with a 1:1 ratio are considered). Our goal is to understand if there is hope for better results in between these two extremes. To this end, we consider restricted graph classes which allow us to characterize the distributions of sensitive attributes for which this form of fairness is tractable from a complexity point of view. While existing work on Fair Correlation Clustering gives approximation algorithms, we focus on exact solutions and investigate whether there are efficiently solvable instances. The unfair version of Correlation Clustering is trivial on forests, but adding fairness creates a surprisingly rich picture of complexities. We give an overview of the distributions and types of forests where Fair Correlation Clustering turns from tractable to intractable. As the most surprising insight, we consider the fact that the cause of the hardness of Fair Correlation Clustering is not the strictness of the fairness condition. We lift most of our results to also hold for the relaxed version of the fairness condition. Instead, the source of hardness seems to be the distribution of the sensitive attribute. On the positive side, we identify some reasonable distributions that are indeed tractable. While this tractability is only shown for forests, it may open an avenue to design reasonable approximations for larger graph classes.
@inproceedings{case2023correlation, abstract = {The study of algorithmic fairness received growing attention recently. This stems from the awareness that bias in the input data for machine learning systems may result in discriminatory outputs. For clustering tasks, one of the most central notions of fairness is the formalization by Chierichetti, Kumar, Lattanzi, and Vassilvitskii [NeurIPS 2017]. A clustering is said to be fair, if each cluster has the same distribution of manifestations of a sensitive attribute as the whole input set. This is motivated by various applications where the objects to be clustered have sensitive attributes that should not be over- or underrepresented. Most research on this version of fair clustering has focused on centriod-based objectives. In contrast, we discuss the applicability of this fairness notion to Correlation Clustering. The existing literature on the resulting Fair Correlation Clustering problem either presents approximation algorithms with poor approximation guarantees or severely limits the possible distributions of the sensitive attribute (often only two manifestations with a 1:1 ratio are considered). Our goal is to understand if there is hope for better results in between these two extremes. To this end, we consider restricted graph classes which allow us to characterize the distributions of sensitive attributes for which this form of fairness is tractable from a complexity point of view. While existing work on Fair Correlation Clustering gives approximation algorithms, we focus on exact solutions and investigate whether there are efficiently solvable instances. The unfair version of Correlation Clustering is trivial on forests, but adding fairness creates a surprisingly rich picture of complexities. We give an overview of the distributions and types of forests where Fair Correlation Clustering turns from tractable to intractable. As the most surprising insight, we consider the fact that the cause of the hardness of Fair Correlation Clustering is not the strictness of the fairness condition. We lift most of our results to also hold for the relaxed version of the fairness condition. Instead, the source of hardness seems to be the distribution of the sensitive attribute. On the positive side, we identify some reasonable distributions that are indeed tractable. While this tractability is only shown for forests, it may open an avenue to design reasonable approximations for larger graph classes.}, author = {Casel, Katrin and Friedrich, Tobias and Schirneck, Martin and Wietheger, Simon}, booktitle = {Foundations of Responsible Computing (FORC)}, keywords = {katrincasel simonwietheger forc tobiasfriedrich year2023 martinschirneck}, pages = {9:1-9:12}, title = {Fair Correlation Clustering in Forests}, year = 2023 }

Jansen, Bart M. P.; Khazaliya, Liana; Kindermann, Philipp; Liotta, Giuseppe; Montecchiani, Fabrizio; Simonov, Kirill Upward and Orthogonal Planarity are W[1]-Hard Parameterized by TreewidthGraph Drawing (GD) 2023: 203–217
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Upward planarity testing and Rectilinear planarity testing are central problems in graph drawing. It is known that they are both NP-complete, but XP when parameterized by treewidth. In this paper we show that these two problems are W[1]-hard parameterized by treewidth, which answers open problems posed in two earlier papers. The key step in our proof is an analysis of the All-or-Nothing Flow problem, a generalization of which was used as an intermediate step in the NP-completeness proof for both planarity testing problems. We prove that the flow problem is W[1]-hard parameterized by treewidth on planar graphs, and that the existing chain of reductions to the planarity testing problems can be adapted without blowing up the treewidth. Our reductions also show that the known \(n^{\mathcal{O(tw)}\)-time algorithms cannot be improved to run in time \(n^{o(tw)}\) unless ETH fails.
@inproceedings{DBLP:conf/gd/JansenKKLMS23, abstract = {Upward planarity testing and Rectilinear planarity testing are central problems in graph drawing. It is known that they are both NP-complete, but XP when parameterized by treewidth. In this paper we show that these two problems are W[1]-hard parameterized by treewidth, which answers open problems posed in two earlier papers. The key step in our proof is an analysis of the All-or-Nothing Flow problem, a generalization of which was used as an intermediate step in the NP-completeness proof for both planarity testing problems. We prove that the flow problem is W[1]-hard parameterized by treewidth on planar graphs, and that the existing chain of reductions to the planarity testing problems can be adapted without blowing up the treewidth. Our reductions also show that the known \(n^{\mathcal{O}(tw)}\)-time algorithms cannot be improved to run in time \(n^{o(tw)}\) unless ETH fails.}, author = {Jansen, Bart M. P. and Khazaliya, Liana and Kindermann, Philipp and Liotta, Giuseppe and Montecchiani, Fabrizio and Simonov, Kirill}, booktitle = {Graph Drawing (GD)}, keywords = {kirillsimonov year2023 gd}, pages = {203&ndash;217}, title = {Upward and Orthogonal Planarity are W[1]-Hard Parameterized by Treewidth}, year = 2023 }

Baguley, Samuel; Friedrich, Tobias; Neumann, Aneta; Neumann, Frank; Pappik, Marcus; Zeif, Ziena Fixed Parameter Multi-Objective Evolutionary Algorithms for the W-Separator ProblemGenetic and Evolutionary Computation Conference (GECCO) 2023
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Parameterized analysis provides powerful mechanisms for obtaining fine-grained insights into different types of algorithms. In this work, we combine this field with evolutionary algorithms and provide parameterized complexity analysis of evolutionary multi-objective algorithms for the W-separator problem, which is a natural generalization of the vertex cover problem. The goal is to remove the minimum number of vertices such that each connected component in the resulting graph has at most W vertices. We provide different multi-objective formulations involving two or three objectives that provably lead to fixed-parameter evolutionary algorithms with respect to the value of an optimal solution OPT and W. Of particular interest are kernelizations and the reducible structures used for them. We show that in expectation the algorithms make incremental progress in finding such structures and beyond. The current best known kernelization of the W-separator uses linear programming methods and requires a non-trivial post-process to extract the reducible structures. We provide additional structural features to show that evolutionary algorithms with appropriate objectives are also capable of extracting them. Our results show that evolutionary algorithms with different objectives guide the search and admit fixed parameterized runtimes to solve or approximate (even arbitrarily close) the W-separator problem.
@inproceedings{baguley2023fixed, abstract = {Parameterized analysis provides powerful mechanisms for obtaining fine-grained insights into different types of algorithms. In this work, we combine this field with evolutionary algorithms and provide parameterized complexity analysis of evolutionary multi-objective algorithms for the W-separator problem, which is a natural generalization of the vertex cover problem. The goal is to remove the minimum number of vertices such that each connected component in the resulting graph has at most W vertices. We provide different multi-objective formulations involving two or three objectives that provably lead to fixed-parameter evolutionary algorithms with respect to the value of an optimal solution OPT and W. Of particular interest are kernelizations and the reducible structures used for them. We show that in expectation the algorithms make incremental progress in finding such structures and beyond. The current best known kernelization of the W-separator uses linear programming methods and requires a non-trivial post-process to extract the reducible structures. We provide additional structural features to show that evolutionary algorithms with appropriate objectives are also capable of extracting them. Our results show that evolutionary algorithms with different objectives guide the search and admit fixed parameterized runtimes to solve or approximate (even arbitrarily close) the W-separator problem.}, author = {Baguley, Samuel and Friedrich, Tobias and Neumann, Aneta and Neumann, Frank and Pappik, Marcus and Zeif, Ziena}, booktitle = {Genetic and Evolutionary Computation Conference (GECCO)}, keywords = {anetaneumann sys:relevantfor:ae zienazeif marcuspappik samuelbaguley tobiasfriedrich gecco frankneumann year2023}, title = {Fixed Parameter Multi-Objective Evolutionary Algorithms for the W-Separator Problem}, year = 2023 }

Li, Xiaoyue; Kötzing, Timo Experimental Analyses of Crossover on JumpGenetic and Evolutionary Computation Conference (GECCO) 2023
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While it is mathematically proven that the \((\mu+1)\) GA optimizes \(\mathrm{jump}_{k}\) efficiently for low crossover probabilities, theory research still struggles with the analysis of crossover-based optimization for high crossover probabilities on this key test function. Research in this area has improved our understanding of crossover in general, in particular regarding the emergence of diversity, the crucial ingredient for successful optimization with genetic algorithms. In this paper we study the optimizing process after the \((\mu+1)\) GA has reached the plateau of \(\mathrm{jump}_{k}\). We are interested in (a) the stationary distribution of the algorithm on the plateau (when ignoring the optimum) and (b) the dynamics of the stationary distribution. We experimentally show that the \((\mu+1)\) GA achieves 10% complementary pairs if \(\mu = 10 \cdot k\), unless \(n\) is very small. Regarding the dynamics, we show samples of how bit positions gain and lose individuals with a \(0\) at that position.
@inproceedings{friedrich2023analysis, abstract = {While it is mathematically proven that the \((\mu+1)\) GA optimizes \(\mathrm{jump}_{k}\) efficiently for low crossover probabilities, theory research still struggles with the analysis of crossover-based optimization for high crossover probabilities on this key test function. Research in this area has improved our understanding of crossover in general, in particular regarding the emergence of diversity, the crucial ingredient for successful optimization with genetic algorithms. In this paper we study the optimizing process after the \((\mu+1)\) GA has reached the plateau of \(\mathrm{jump}_{k}\). We are interested in (a) the stationary distribution of the algorithm on the plateau (when ignoring the optimum) and (b) the dynamics of the stationary distribution. We experimentally show that the \((\mu+1)\) GA achieves 10\% complementary pairs if \(\mu = 10 \cdot k\), unless \(n\) is very small. Regarding the dynamics, we show samples of how bit positions gain and lose individuals with a \(0\) at that position.}, author = {Li, Xiaoyue and Kötzing, Timo}, booktitle = {Genetic and Evolutionary Computation Conference (GECCO)}, keywords = {xiaoyueli timokoetzing gecco year2023}, title = {Experimental Analyses of Crossover on Jump}, year = 2023 }

Nikfarjam, Adel; Rothenberger, Ralf; Neumann, Frank; Friedrich, Tobias Evolutionary Diversity Optimisation in Constructing Satisfying AssignmentsGenetic and Evolutionary Computation Conference (GECCO) 2023
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Computing diverse solutions for a given problem, in particular evolutionary diversity optimisation (EDO), is a hot research topic in the evolutionary computation community. This paper studies the Boolean satisfiability problem (SAT) in the context of EDO. SAT is an of great importance in computer science and differs from the other problems that have been studied in EDO literature, such as KP and TSP. 1) it is possible to add more constraints (clauses) to the problem so as to forbid solutions or fix variables. 2) There can be found several powerful solvers in the literature such as minisat; we utilise such a solver to construct a diverse set of solutions. Moreover, maximising diversity provides us with invaluable information about the solution space of a given SAT problem, such as how large is the feasible region. In this study, we introduce evolutionary algorithms (EAs) employing a well-known SAT solver to maximise diversity among a set of SAT solutions explicitly. The experimental investigations indicate the introduced algorithms' capability to maximise diversity among the SAT solutions.
@inproceedings{nikfarjam2023evolutionary, abstract = {Computing diverse solutions for a given problem, in particular evolutionary diversity optimisation (EDO), is a hot research topic in the evolutionary computation community. This paper studies the Boolean satisfiability problem (SAT) in the context of EDO. SAT is an of great importance in computer science and differs from the other problems that have been studied in EDO literature, such as KP and TSP. 1) it is possible to add more constraints (clauses) to the problem so as to forbid solutions or fix variables. 2) There can be found several powerful solvers in the literature such as minisat; we utilise such a solver to construct a diverse set of solutions. Moreover, maximising diversity provides us with invaluable information about the solution space of a given SAT problem, such as how large is the feasible region. In this study, we introduce evolutionary algorithms (EAs) employing a well-known SAT solver to maximise diversity among a set of SAT solutions explicitly. The experimental investigations indicate the introduced algorithms' capability to maximise diversity among the SAT solutions.}, author = {Nikfarjam, Adel and Rothenberger, Ralf and Neumann, Frank and Friedrich, Tobias}, booktitle = {Genetic and Evolutionary Computation Conference (GECCO)}, keywords = {sys:relevantfor:ae tobiasfriedrich gecco frankneumann year2023 adelnikfarjam ralfrothenberger}, title = {Evolutionary Diversity Optimisation in Constructing Satisfying Assignments}, year = 2023 }

Friedrich, Tobias; Kötzing, Timo; Neumann, Aneta; Neumann, Frank; Radhakrishnan, Aishwarya Analysis of the (1+1) EA on LeadingOnes with ConstraintsGenetic and Evolutionary Computation Conference (GECCO ’23) 2023
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Understanding how evolutionary algorithms perform on constrained problems has gained increasing attention in recent years. In this paper, we study how evolutionary algorithms optimize constrained versions of the classical LeadingOnes problem. We first provide a run time analysis for the classical (1+1)~EA on the LeadingOnes problem with a deterministic cardinality constraint, giving \($\Theta(n (n-B)\log(B) + n^2)$\) as the tight bound. Our results show that the behaviour of the algorithm is highly dependent on the constraint bound of the uniform constraint. Afterwards, we consider the problem in the context of stochastic constraints and provide insights using experimental studies on how the (\($\mu$\)+1)~EA is able to deal with these constraints in a sampling-based setting.
@inproceedings{friedrich2023analysis, abstract = {Understanding how evolutionary algorithms perform on constrained problems has gained increasing attention in recent years. In this paper, we study how evolutionary algorithms optimize constrained versions of the classical LeadingOnes problem. We first provide a run time analysis for the classical (1+1)&nbsp;EA on the LeadingOnes problem with a deterministic cardinality constraint, giving $\Theta(n (n-B)\log(B) + n^2)$ as the tight bound. Our results show that the behaviour of the algorithm is highly dependent on the constraint bound of the uniform constraint. Afterwards, we consider the problem in the context of stochastic constraints and provide insights using experimental studies on how the ($\mu$+1)&nbsp;EA is able to deal with these constraints in a sampling-based setting.}, author = {Friedrich, Tobias and Kötzing, Timo and Neumann, Aneta and Neumann, Frank and Radhakrishnan, Aishwarya}, booktitle = {Genetic and Evolutionary Computation Conference (GECCO '23)}, keywords = {aishwaryaradhakrishnan timokoetzing tobiasfriedrich gecco year2023}, title = {Analysis of the (1+1) EA on LeadingOnes with Constraints}, year = 2023 }

Bilò, Davide; Choudhary, Keerti; Cohen, Sarel; Friedrich, Tobias; Krogmann, Simon; Schirneck, Martin Fault-Tolerant ST-Diameter OraclesInternational Colloquium on Automata, Languages and Programming (ICALP) 2023: 24:1–24:20
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We study the problem of estimating the \(ST\)-diameter of a graph that is subject to a bounded number of edge failures. An \(f\)-edge fault-tolerant \(ST\)-diameter oracle (\(f\)-FDO-\(ST\)) is a data structure that preprocesses a given graph \(G\), two sets of vertices \(S,T\), and positive integer \(f\). When queried with a set \(F\) of at most \(f\) edges, the oracle returns an estimate \(\widehat{D}\) of the \(ST\)-diameter \(\mathrm{diam(G-F,S,T)\), the maximum distance between vertices in \(S\) and \(T\) in \(G-F\). The oracle has stretch \(\sigma \geq 1\) if \(\mathrm{diam(G-F,S,T) leq \widehat{D leq sigma \mathrm{diam(G-F,S,T)\). If \(S\) and \(T\) both contain all vertices, the data structure is called an \(f\)-edge fault-tolerant diameter oracle (\(f\)-FDO). An \(f\)-edge fault-tolerant distance sensitivity oracles (\(f\)-DSO) estimates the pairwise graph distances under up to \(f\) failures. We design new \(f\)-FDOs and \(f\)-FDO-\(ST\)s by reducing their construction to that of all-pairs and single-source \(f\)-DSOs. We obtain several new tradeoffs between the size of the data structure, stretch guarantee, query and preprocessing times for diameter oracles by combining our black-box reductions with known results from the literature. We also provide an information-theoretic lower bound on the space requirement of approximate \(f\)-FDOs. We show that there exists a family of graphs for which any \(f\)-FDO with sensitivity \(f \ge 2\) and stretch less than \(5/3\) requires \(\Omega(n^{3/2})\) bits of space, regardless of the query time.
@inproceedings{bilo2023faulttolerant, abstract = {We study the problem of estimating the \(ST\)-diameter of a graph that is subject to a bounded number of edge failures. An \(f\)-edge fault-tolerant \(ST\)-diameter oracle (\(f\)-FDO-\(ST\)) is a data structure that preprocesses a given graph \(G\), two sets of vertices \(S,T\), and positive integer \(f\). When queried with a set \(F\) of at most \(f\) edges, the oracle returns an estimate \(\widehat{D}\) of the \(ST\)-diameter \(\mathrm{diam}(G-F,S,T)\), the maximum distance between vertices in \(S\) and \(T\) in \(G-F\). The oracle has stretch \(\sigma \geq 1\) if \(\mathrm{diam}(G-F,S,T) \leq \widehat{D} \leq \sigma \mathrm{diam}(G-F,S,T)\). If \(S\) and \(T\) both contain all vertices, the data structure is called an \(f\)-edge fault-tolerant diameter oracle (\(f\)-FDO). An \(f\)-edge fault-tolerant distance sensitivity oracles (\(f\)-DSO) estimates the pairwise graph distances under up to \(f\) failures. We design new \(f\)-FDOs and \(f\)-FDO-\(ST\)s by reducing their construction to that of all-pairs and single-source \(f\)-DSOs. We obtain several new tradeoffs between the size of the data structure, stretch guarantee, query and preprocessing times for diameter oracles by combining our black-box reductions with known results from the literature. We also provide an information-theoretic lower bound on the space requirement of approximate \(f\)-FDOs. We show that there exists a family of graphs for which any \(f\)-FDO with sensitivity \(f \ge 2\) and stretch less than \(5/3\) requires \(\Omega(n^{3/2})\) bits of space, regardless of the query time.}, author = {Bilò, Davide and Choudhary, Keerti and Cohen, Sarel and Friedrich, Tobias and Krogmann, Simon and Schirneck, Martin}, booktitle = {International Colloquium on Automata, Languages and Programming (ICALP)}, keywords = {sarelcohen davidebilo tobiasfriedrich year2023 icalp keertichoudhary simonkrogmann martinschirneck}, pages = {24:1-24:20}, title = {Fault-Tolerant ST-Diameter Oracles}, year = 2023 }

Fomin, Fedor; Golovach, Petr; Sagunov, Danil; Simonov, Kirill Approximating Long Cycle Above Dirac’s GuaranteeInternational Colloquium on Automata, Languages and Programming (ICALP) 2023: 60:1–60:18
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Parameterization above (or below) a guarantee is a successful concept in parameterized algorithms. The idea is that many computational problems admit “natural” guarantees bringing to algorithmic questions whether a better solution (above the guarantee) could be obtained efficiently. For example, for every boolean CNF formula on m clauses, there is an assignment that satisfies at least m/2 clauses. How difficult is it to decide whether there is an assignment satisfying more than m/2 + k clauses? Or, if an n-vertex graph has a perfect matching, then its vertex cover is at least n/2. Is there a vertex cover of size at least n/2 + k for some \(k \geq 1\) and how difficult is it to find such a vertex cover? The above guarantee paradigm has led to several exciting discoveries in the areas of parameterized algorithms and kernelization. We argue that this paradigm could bring forth fresh perspectives on well-studied problems in approximation algorithms. Our example is the longest cycle problem. One of the oldest results in extremal combinatorics is the celebrated Dirac’s theorem from 1952. Dirac’s theorem provides the following guarantee on the length of the longest cycle: for every 2-connected n-vertex graph G with minimum degree \(\delta(G) \leq n/2\), the length of a longest cycle L is at least \(2\delta(G)\). Thus the “essential” part in finding the longest cycle is in approximating the “offset” \(k = L − 2\delta(G)\). The main result of this paper is the above-guarantee approximation theorem for k. Informally, the theorem says that approximating the offset k is not harder than approximating the total length L of a cycle. In other words, for any (reasonably well-behaved) function f, a polynomial time algorithm constructing a cycle of length f(L) in an undirected graph with a cycle of length L, yields a polynomial time algorithm constructing a cycle of length \(2\delta(G) + \Omega(f(k))\).
@inproceedings{fomin2023approximating, abstract = {Parameterization above (or below) a guarantee is a successful concept in parameterized algorithms. The idea is that many computational problems admit “natural” guarantees bringing to algorithmic questions whether a better solution (above the guarantee) could be obtained efficiently. For example, for every boolean CNF formula on m clauses, there is an assignment that satisfies at least m/2 clauses. How difficult is it to decide whether there is an assignment satisfying more than m/2 + k clauses? Or, if an n-vertex graph has a perfect matching, then its vertex cover is at least n/2. Is there a vertex cover of size at least n/2 + k for some \(k \geq 1\) and how difficult is it to find such a vertex cover? The above guarantee paradigm has led to several exciting discoveries in the areas of parameterized algorithms and kernelization. We argue that this paradigm could bring forth fresh perspectives on well-studied problems in approximation algorithms. Our example is the longest cycle problem. One of the oldest results in extremal combinatorics is the celebrated Dirac’s theorem from 1952. Dirac’s theorem provides the following guarantee on the length of the longest cycle: for every 2-connected n-vertex graph G with minimum degree \(\delta(G) \leq n/2\), the length of a longest cycle L is at least \(2\delta(G)\). Thus the “essential” part in finding the longest cycle is in approximating the “offset” \(k = L − 2\delta(G)\). The main result of this paper is the above-guarantee approximation theorem for k. Informally, the theorem says that approximating the offset k is not harder than approximating the total length L of a cycle. In other words, for any (reasonably well-behaved) function f, a polynomial time algorithm constructing a cycle of length f(L) in an undirected graph with a cycle of length L, yields a polynomial time algorithm constructing a cycle of length \(2\delta(G) + \Omega(f(k))\).}, author = {Fomin, Fedor and Golovach, Petr and Sagunov, Danil and Simonov, Kirill}, booktitle = {International Colloquium on Automata, Languages and Programming (ICALP)}, keywords = {sys:relevantfor:ae kirillsimonov year2023 icalp}, pages = {60:1&ndash;60:18}, title = {Approximating Long Cycle Above Dirac’s Guarantee}, year = 2023 }

Friedrich, Tobias; Göbel, Andreas; Katzmann, Maximilian; Schiller, Leon Cliques in High-Dimensional Geometric Inhomogeneous Random GraphsInternational Colloquium on Automata, Languages and Programming (ICALP) 2023: 62:1–62:13
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
A recent trend in the context of graph theory is to bring theoretical analyses closer to empirical observations, by focusing the studies on random graph models that are used to represent practical instances. There, it was observed that geometric inhomogeneous random graphs (GIRGs) yield good representations of complex real-world networks, by expressing edge probabilities as a function that depends on (heterogeneous) vertex weights and distances in some underlying geometric space that the vertices are distributed in. While most of the parameters of the model are understood well, it was unclear how the dimensionality of the ground space affects the structure of the graphs. In this paper, we complement existing research into the dimension of geometric random graph models and the ongoing study of determining the dimensionality of real-world networks, by studying how the structure of GIRGs changes as the number of dimensions increases. We prove that, in the limit, GIRGs approach non-geometric inhomogeneous random graphs and present insights on how quickly the decay of the geometry impacts important graph structures. In particular, we study the expected number of cliques of a given size as well as the clique number and characterize phase transitions at which their behavior changes fundamentally. Finally, our insights help in better understanding previous results about the impact of the dimensionality on geometric random graphs.
@inproceedings{friedrich2023cliques, abstract = {A recent trend in the context of graph theory is to bring theoretical analyses closer to empirical observations, by focusing the studies on random graph models that are used to represent practical instances. There, it was observed that geometric inhomogeneous random graphs (GIRGs) yield good representations of complex real-world networks, by expressing edge probabilities as a function that depends on (heterogeneous) vertex weights and distances in some underlying geometric space that the vertices are distributed in. While most of the parameters of the model are understood well, it was unclear how the dimensionality of the ground space affects the structure of the graphs. In this paper, we complement existing research into the dimension of geometric random graph models and the ongoing study of determining the dimensionality of real-world networks, by studying how the structure of GIRGs changes as the number of dimensions increases. We prove that, in the limit, GIRGs approach non-geometric inhomogeneous random graphs and present insights on how quickly the decay of the geometry impacts important graph structures. In particular, we study the expected number of cliques of a given size as well as the clique number and characterize phase transitions at which their behavior changes fundamentally. Finally, our insights help in better understanding previous results about the impact of the dimensionality on geometric random graphs.}, author = {Friedrich, Tobias and Göbel, Andreas and Katzmann, Maximilian and Schiller, Leon}, booktitle = {International Colloquium on Automata, Languages and Programming (ICALP)}, keywords = {sys:relevantfor:ae andreasgoebel tobiasfriedrich leonschiller year2023 icalp maximiliankatzmann}, pages = {62:1&ndash;62:13}, title = {Cliques in High-Dimensional Geometric Inhomogeneous Random Graphs}, year = 2023 }

Bilò, Davide; Cohen, Sarel; Friedrich, Tobias; Gawendowicz, Hans; Klodt, Nicolas; Lenzner, Pascal; Skretas, George Temporal Network Creation GamesInternational Joint Conference on Artificial Intelligence (IJCAI) 2023: 2511–2519
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Most networks are not static objects, but instead they change over time. This observation has sparked rigorous research on temporal graphs within the last years. In temporal graphs, we have a fixed set of nodes and the connections between them are only available at certain time steps. This gives rise to a plethora of algorithmic problems on such graphs, most prominently the problem of finding temporal spanners, i.e., the computation of subgraphs that guarantee all pairs reachability via temporal paths. To the best of our knowledge, only centralized approaches for the solution of this problem are known. However, many real-world networks are not shaped by a central designer but instead they emerge and evolve by the interaction of many strategic agents. This observation is the driving force of the recent intensive research on game-theoretic network formation models. In this work we bring together these two recent research directions: temporal graphs and game-theoretic network formation. As a first step into this new realm, we focus on a simplified setting where a complete temporal host graph is given and the agents, corresponding to its nodes, selfishly create incident edges to ensure that they can reach all other nodes via temporal paths in the created network. This yields temporal spanners as equilibria of our game. We prove results on the convergence to and the existence of equilibrium networks, on the complexity of finding best agent strategies, and on the quality of the equilibria. By taking these first important steps, we uncover challenging open problems that call for an in-depth exploration of the creation of temporal graphs by strategic agents.
@inproceedings{bilo2023temporal, abstract = {Most networks are not static objects, but instead they change over time. This observation has sparked rigorous research on temporal graphs within the last years. In temporal graphs, we have a fixed set of nodes and the connections between them are only available at certain time steps. This gives rise to a plethora of algorithmic problems on such graphs, most prominently the problem of finding temporal spanners, i.e., the computation of subgraphs that guarantee all pairs reachability via temporal paths. To the best of our knowledge, only centralized approaches for the solution of this problem are known. However, many real-world networks are not shaped by a central designer but instead they emerge and evolve by the interaction of many strategic agents. This observation is the driving force of the recent intensive research on game-theoretic network formation models. In this work we bring together these two recent research directions: temporal graphs and game-theoretic network formation. As a first step into this new realm, we focus on a simplified setting where a complete temporal host graph is given and the agents, corresponding to its nodes, selfishly create incident edges to ensure that they can reach all other nodes via temporal paths in the created network. This yields temporal spanners as equilibria of our game. We prove results on the convergence to and the existence of equilibrium networks, on the complexity of finding best agent strategies, and on the quality of the equilibria. By taking these first important steps, we uncover challenging open problems that call for an in-depth exploration of the creation of temporal graphs by strategic agents.}, author = {Bilò, Davide and Cohen, Sarel and Friedrich, Tobias and Gawendowicz, Hans and Klodt, Nicolas and Lenzner, Pascal and Skretas, George}, booktitle = {International Joint Conference on Artificial Intelligence (IJCAI)}, keywords = {ijcai sarelcohen hansgawendowicz nicolasklodt tobiasfriedrich year2023 pascallenzner georgeskretas}, pages = {2511&ndash;2519}, title = {Temporal Network Creation Games}, year = 2023 }

Bilò, Davide; Bilò, Vittorio; Döring, Michelle; Lenzner, Pascal; Molitor, Louise; Schmidt, Jonas Schelling Games with Continuous TypesInternational Joint Conference on Artificial Intelligence (IJCAI) 2023: 2520–2527
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In most major cities and urban areas, residents form homogeneous neighborhoods along ethnic or socioeconomic lines. This phenomenon is widely known as residential segregation and has been studied extensively. Fifty years ago, Schelling proposed a landmark model that explains residential segregation in an elegant agent-based way. A recent stream of papers analyzed Schelling’s model using game-theoretic approaches. However, all these works considered models with a given number of discrete types modeling different ethnic groups. We focus on segregation caused by non-categorical attributes, such as household income or position in a political left-right spectrum. For this, we consider agent types that can be represented as real numbers. This opens up a great variety of reasonable models and, as a proof of concept, we focus on several natural candidates. In particular, we consider agents that evaluate their location by the average type-difference or the maximum type-difference to their neighbors, or by having a certain tolerance range for type-values of neighboring agents. We study the existence and computation of equilibria and provide bounds on the Price of Anarchy and Stability. Also, we present simulation results that compare our models and shed light on the obtained equilibria for our variants.
@inproceedings{bilo2023continuous, abstract = {In most major cities and urban areas, residents form homogeneous neighborhoods along ethnic or socioeconomic lines. This phenomenon is widely known as residential segregation and has been studied extensively. Fifty years ago, Schelling proposed a landmark model that explains residential segregation in an elegant agent-based way. A recent stream of papers analyzed Schelling’s model using game-theoretic approaches. However, all these works considered models with a given number of discrete types modeling different ethnic groups. We focus on segregation caused by non-categorical attributes, such as household income or position in a political left-right spectrum. For this, we consider agent types that can be represented as real numbers. This opens up a great variety of reasonable models and, as a proof of concept, we focus on several natural candidates. In particular, we consider agents that evaluate their location by the average type-difference or the maximum type-difference to their neighbors, or by having a certain tolerance range for type-values of neighboring agents. We study the existence and computation of equilibria and provide bounds on the Price of Anarchy and Stability. Also, we present simulation results that compare our models and shed light on the obtained equilibria for our variants.}, author = {Bilò, Davide and Bilò, Vittorio and Döring, Michelle and Lenzner, Pascal and Molitor, Louise and Schmidt, Jonas}, booktitle = {International Joint Conference on Artificial Intelligence (IJCAI)}, keywords = {ijcai louisemolitor year2023 michelledoering pascallenzner}, pages = {2520&ndash;2527}, title = {Schelling Games with Continuous Types}, year = 2023 }

Gadea Harder, Jonathan; Krogmann, Simon; Lenzner, Pascal; Skopalik, Alexander Strategic Resource Selection with Homophilic AgentsInternational Joint Conference on Artificial Intelligence (IJCAI) 2023: 2701–2709
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
The strategic selection of resources by selfish agents is a classic research direction, with Resource Selection Games and Congestion Games as prominent examples. In these games, agents select available resources and their utility then depends on the number of agents using the same resources. This implies that there is no distinction between the agents, i.e., they are anonymous. We depart from this very general setting by proposing Resource Selection Games with heterogeneous agents that strive for joint resource usage with similar agents. So, instead of the number of other users of a given resource, our model considers agents with different types and the decisive feature is the fraction of same-type agents among the users. More precisely, similarly to Schelling Games, there is a tolerance threshold \(\tau \in [0,1]\) which specifies the agents' desired minimum fraction of same-type agents on a resource. Agents strive to select resources where at least a \(\tau\)-fraction of those resources' users have the same type as themselves. For \(\tau=1\), our model generalizes Hedonic Diversity Games with a peak at \(1\). For our general model, we consider the existence and quality of equilibria and the complexity of maximizing social welfare. Additionally, we consider a bounded rationality model, where agents can only estimate the utility of a resource, since they only know the fraction of same-type agents on a given resource, but not the exact numbers. Thus, they cannot know the impact a strategy change would have on a target resource. Interestingly, we show that this type of bounded rationality yields favorable game-theoretic properties and specific equilibria closely approximate equilibria of the full knowledge setting.
@inproceedings{gadeaharder2023strategic, abstract = {The strategic selection of resources by selfish agents is a classic research direction, with Resource Selection Games and Congestion Games as prominent examples. In these games, agents select available resources and their utility then depends on the number of agents using the same resources. This implies that there is no distinction between the agents, i.e., they are anonymous. We depart from this very general setting by proposing Resource Selection Games with heterogeneous agents that strive for joint resource usage with similar agents. So, instead of the number of other users of a given resource, our model considers agents with different types and the decisive feature is the fraction of same-type agents among the users. More precisely, similarly to Schelling Games, there is a tolerance threshold \(\tau \in [0,1]\) which specifies the agents' desired minimum fraction of same-type agents on a resource. Agents strive to select resources where at least a \(\tau\)-fraction of those resources' users have the same type as themselves. For \(\tau=1\), our model generalizes Hedonic Diversity Games with a peak at \(1\). For our general model, we consider the existence and quality of equilibria and the complexity of maximizing social welfare. Additionally, we consider a bounded rationality model, where agents can only estimate the utility of a resource, since they only know the fraction of same-type agents on a given resource, but not the exact numbers. Thus, they cannot know the impact a strategy change would have on a target resource. Interestingly, we show that this type of bounded rationality yields favorable game-theoretic properties and specific equilibria closely approximate equilibria of the full knowledge setting.}, author = {Gadea Harder, Jonathan and Krogmann, Simon and Lenzner, Pascal and Skopalik, Alexander}, booktitle = {International Joint Conference on Artificial Intelligence (IJCAI)}, keywords = {ijcai year2023 simonkrogmann pascallenzner jonathangadeaharder}, pages = {2701-2709}, title = {Strategic Resource Selection with Homophilic Agents}, year = 2023 }

Deligkas, Argyrios; Eiben, Eduard; Skretas, George Minimizing Reachability Times on Temporal Graphs via Shifting LabelsInternational Joint Conference on Artificial Intelligence (IJCAI) 2023: 5333–5340
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
We study how we can accelerate the spreading of information in temporal graphs via delaying operations; a problem that captures real-world applications varying from information flows to distribution schedules. In a temporal graph there is a set of fixed vertices and the available connections between them change over time in a predefined manner. We observe that, in some cases, the delay of some connections can in fact decrease the time required to reach from some vertex (source) to another vertex (target). We study how we can minimize the maximum time a set of source vertices needs to reach every other vertex of the graph when we are allowed to delay some of the connections of the graph. For one source, we prove that the problem is W[2]-hard and NP-hard, when parameterized by the number of allowed delays. On the other hand, we derive a polynomial-time algorithm for one source and unbounded number of delays. This is the best we can hope for; we show that the problem becomes NP-hard when there are two sources and the number of delays is not bounded. We complement our negative result by providing an FPT algorithm parameterized by the treewidth of the graph plus the lifetime of the optimal solution. Finally, we provide polynomial-time algorithms for several classes of graphs.
@inproceedings{deligkas2023minimizing, abstract = {We study how we can accelerate the spreading of information in temporal graphs via delaying operations; a problem that captures real-world applications varying from information flows to distribution schedules. In a temporal graph there is a set of fixed vertices and the available connections between them change over time in a predefined manner. We observe that, in some cases, the delay of some connections can in fact decrease the time required to reach from some vertex (source) to another vertex (target). We study how we can minimize the maximum time a set of source vertices needs to reach every other vertex of the graph when we are allowed to delay some of the connections of the graph. For one source, we prove that the problem is W[2]-hard and NP-hard, when parameterized by the number of allowed delays. On the other hand, we derive a polynomial-time algorithm for one source and unbounded number of delays. This is the best we can hope for; we show that the problem becomes NP-hard when there are two sources and the number of delays is not bounded. We complement our negative result by providing an FPT algorithm parameterized by the treewidth of the graph plus the lifetime of the optimal solution. Finally, we provide polynomial-time algorithms for several classes of graphs.}, author = {Deligkas, Argyrios and Eiben, Eduard and Skretas, George}, booktitle = {International Joint Conference on Artificial Intelligence (IJCAI)}, keywords = {ijcai myown sys:relevantfor:ae year2023 georgeskretas}, pages = {5333&ndash;5340}, title = {Minimizing Reachability Times on Temporal Graphs via Shifting Labels}, year = 2023 }

Ganian, Robert; Khazaliya, Liana; Simonov, Kirill Consistency Checking Problems: A Gateway to Parameterized Sample ComplexityInternational Symposium on Parameterized and Exact Computation (IPEC) 2023: 18:1–18:17
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Recently, Brand, Ganian and Simonov introduced a parameterized refinement of the classical PAC-learning sample complexity framework. A crucial outcome of their investigation is that for a very wide range of learning problems, there is a direct and provable correspondence between fixed-parameter PAC-learnability (in the sample complexity setting) and the fixed-parameter tractability of a corresponding “consistency checking” search problem (in the setting of computational complexity). The latter can be seen as generalizations of classical search problems where instead of receiving a single instance, one receives multiple yes- and no-examples and is tasked with finding a solution which is consistent with the provided examples. Apart from a few initial results, consistency checking problems are almost entirely unexplored from a parameterized complexity perspective. In this article, we provide an overview of these problems and their connection to parameterized sample complexity, with the primary aim of facilitating further research in this direction. Afterwards, we establish the fixed-parameter (in)-tractability for some of the arguably most natural consistency checking problems on graphs, and show that their complexity-theoretic behavior is surprisingly very different from that of classical decision problems. Our new results cover consistency checking variants of problems as diverse as (k-)Path, Matching, 2-Coloring, Independent Set and Dominating Set, among others.
@inproceedings{DBLP:conf/iwpec/GanianKS23, abstract = {Recently, Brand, Ganian and Simonov introduced a parameterized refinement of the classical PAC-learning sample complexity framework. A crucial outcome of their investigation is that for a very wide range of learning problems, there is a direct and provable correspondence between fixed-parameter PAC-learnability (in the sample complexity setting) and the fixed-parameter tractability of a corresponding “consistency checking” search problem (in the setting of computational complexity). The latter can be seen as generalizations of classical search problems where instead of receiving a single instance, one receives multiple yes- and no-examples and is tasked with finding a solution which is consistent with the provided examples. Apart from a few initial results, consistency checking problems are almost entirely unexplored from a parameterized complexity perspective. In this article, we provide an overview of these problems and their connection to parameterized sample complexity, with the primary aim of facilitating further research in this direction. Afterwards, we establish the fixed-parameter (in)-tractability for some of the arguably most natural consistency checking problems on graphs, and show that their complexity-theoretic behavior is surprisingly very different from that of classical decision problems. Our new results cover consistency checking variants of problems as diverse as (k-)Path, Matching, 2-Coloring, Independent Set and Dominating Set, among others.}, author = {Ganian, Robert and Khazaliya, Liana and Simonov, Kirill}, booktitle = {International Symposium on Parameterized and Exact Computation (IPEC)}, keywords = {ipec kirillsimonov year2023}, pages = {18:1&ndash;18:17}, title = {Consistency Checking Problems: A Gateway to Parameterized Sample Complexity}, volume = 285, year = 2023 }

Khazaliya, Liana; Kindermann, Philipp; Liotta, Giuseppe; Montecchiani, Fabrizio; Simonov, Kirill The st-Planar Edge Completion Problem Is Fixed-Parameter TractableInternational Symposium Algorithms and Computation (ISAAC) 2023: 46:1–46:13
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
The problem of deciding whether a biconnected planar digraph \(G = (V, E)\) can be augmented to become an st-planar graph by adding a set of oriented edges \(E′ \subseteq V \times V\) is known to be NP-complete. We show that the problem is fixed-parameter tractable when parameterized by the size of the set \(E′\).
@inproceedings{DBLP:conf/isaac/KhazaliyaKLMS23, abstract = {The problem of deciding whether a biconnected planar digraph \(G = (V, E)\) can be augmented to become an st-planar graph by adding a set of oriented edges \(E′ \subseteq V \times V\) is known to be NP-complete. We show that the problem is fixed-parameter tractable when parameterized by the size of the set \(E′\).}, author = {Khazaliya, Liana and Kindermann, Philipp and Liotta, Giuseppe and Montecchiani, Fabrizio and Simonov, Kirill}, booktitle = {International Symposium Algorithms and Computation (ISAAC)}, keywords = {isaac kirillsimonov year2023}, pages = {46:1&ndash;46:13}, title = {The st-Planar Edge Completion Problem Is Fixed-Parameter Tractable}, year = 2023 }

Ashok, Pradeesha; Das, Sayani; Kanesh, Lawqueen; Saurabh, Saket; Tomar, Avi; Verma, Shaily Burn and WinInternational Workshop on Combinatorial Algorithms (IWOCA) 2023: 36–48
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Given a graph \(G\) and an integer \(k\), the graph burning problem asks whether the graph \(G\) can be burned in at most \(k\) rounds. Graph burning is a model for information spreading in a network, where we study how fast the information spreads in the network through its vertices. In each round, the fire is started at an unburned vertex and the fire spreads to all its neighbors in the next round, burning all of them and so on. The minimum number of rounds required to burn the whole graph \(G\) is called the burning number of \(G\). Graph burning problem is NP-hard even for the union of disjoint paths. Moreover, the problem is known to be W[1]-hard when parameterized by the burning number and para-NP-hard when parameterized by treewidth. In this paper, we give a fixed-parameter tractable (FPT) algorithm for graph burning problem when parameterized by treewidth and burning number of the graph. Y. Kobayashi and Y. Otachi [Algorithmica 2022] proved that the problem is FPT parameterized by distance to cographs and gave a double exponential time FPT algorithm when parameterized by distance to split graphs. We improve these results partially and give an FPT algorithm for the problem when parameterized by distance to cographs \(\cap\) split graphs (threshold graphs) that runs in \(2^{\mathcal{O(k\ln k)}\). We also design a kernel for the problem in trees. Furthermore, we give an exact algorithm to find the burning number of a graph that runs in time \(4^n n^\mathcal{O(1)}\), where \(n\) is the number of vertices in the input graph.
@inproceedings{DBLP:conf/iwoca/AshokDK0TV23, abstract = {Given a graph \(G\) and an integer \(k\), the graph burning problem asks whether the graph \(G\) can be burned in at most \(k\) rounds. Graph burning is a model for information spreading in a network, where we study how fast the information spreads in the network through its vertices. In each round, the fire is started at an unburned vertex and the fire spreads to all its neighbors in the next round, burning all of them and so on. The minimum number of rounds required to burn the whole graph \(G\) is called the burning number of \(G\). Graph burning problem is NP-hard even for the union of disjoint paths. Moreover, the problem is known to be W[1]-hard when parameterized by the burning number and para-NP-hard when parameterized by treewidth. In this paper, we give a fixed-parameter tractable (FPT) algorithm for graph burning problem when parameterized by treewidth and burning number of the graph. Y. Kobayashi and Y. Otachi [Algorithmica 2022] proved that the problem is FPT parameterized by distance to cographs and gave a double exponential time FPT algorithm when parameterized by distance to split graphs. We improve these results partially and give an FPT algorithm for the problem when parameterized by distance to cographs \(\cap\) split graphs (threshold graphs) that runs in \(2^{\mathcal{O}(k\ln k)}\). We also design a kernel for the problem in trees. Furthermore, we give an exact algorithm to find the burning number of a graph that runs in time \(4^n n^{\mathcal{O}(1)}\), where \(n\) is the number of vertices in the input graph.}, author = {Ashok, Pradeesha and Das, Sayani and Kanesh, Lawqueen and Saurabh, Saket and Tomar, Avi and Verma, Shaily}, booktitle = {International Workshop on Combinatorial Algorithms (IWOCA)}, keywords = {shailyverma year2023}, pages = {36&ndash;48}, title = {Burn and Win}, year = 2023 }

Bhyravarapu, Sriram; Jana, Satyabrata; Kanesh, Lawqueen; Saurabh, Saket; Verma, Shaily Parameterized Algorithms for Eccentricity Shortest Path ProblemInternational Workshop on Combinatorial Algorithms (IWOCA) 2023: 74–86
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Given an undirected graph \(G=(V,E) \) and an integer \(\ell\), the Eccentricity Shortest Path Problem (ESP) problem asks to check if there exists a shortest path \(P\) such that for every vertex \(vin V(G)\), there is a vertex \(w\in P\) such that \(d_G(v,w)\leq \ell\), where \(d_G(v,w)\) represents the distance between \(v\) and \(w\) in \(G\). Dragan and Leitert [Theor. Comput. Sci. 2017] studied the optimization version of this problem which asks to find the minimum \(\ell\) for ESP and showed that it is sf NP-hard even on planar bipartite graphs with maximum degree 3. They also showed that ESP is sf W[2]-hard when parameterized by \(\ell \). On the positive side, Kucera and Suchy [IWOCA 2021] showed that ESP is fixed-parameter tractable (FPT) when parameterized by modular width, cluster vertex deletion set, maximum leaf number, or the combined parameters disjoint paths deletion set and \( \ell \). It was asked as an open question in the same paper, if ESP is FPT parameterized by disjoint paths deletion set or feedback vertex set. We answer these questions and obtain the following results. We prove that ESP is FPT when parameterized by disjoint paths deletion set, split vertex deletion set, or the combined parameters feedback vertex set and \(\ell\). Moreover, we design a \((1+\epsilon)\)-factor FPT approximation algorithm when parameterized by the feedback vertex set number. We also show that ESP is W[2]-hard when parameterized by the chordal vertex deletion set.
@inproceedings{DBLP:conf/iwoca/BhyravarapuJK0V23, abstract = {Given an undirected graph \(G=(V,E) \) and an integer \(\ell\), the Eccentricity Shortest Path Problem (ESP) problem asks to check if there exists a shortest path \(P\) such that for every vertex \(v\in V(G)\), there is a vertex \(w\in P\) such that \(d_G(v,w)\leq \ell\), where \(d_G(v,w)\) represents the distance between \(v\) and \(w\) in \(G\). Dragan and Leitert [Theor. Comput. Sci. 2017] studied the optimization version of this problem which asks to find the minimum \(\ell\) for ESP and showed that it is {sf NP}-hard even on planar bipartite graphs with maximum degree 3. They also showed that ESP is {sf W}[2]-hard when parameterized by \(\ell \). On the positive side, Kucera and Suchy [IWOCA 2021] showed that ESP is fixed-parameter tractable (FPT) when parameterized by modular width, cluster vertex deletion set, maximum leaf number, or the combined parameters disjoint paths deletion set and \( \ell \). It was asked as an open question in the same paper, if ESP is FPT parameterized by disjoint paths deletion set or feedback vertex set. We answer these questions and obtain the following results. We prove that ESP is FPT when parameterized by disjoint paths deletion set, split vertex deletion set, or the combined parameters feedback vertex set and \(\ell\). Moreover, we design a \((1+\epsilon)\)-factor FPT approximation algorithm when parameterized by the feedback vertex set number. We also show that ESP is W[2]-hard when parameterized by the chordal vertex deletion set.}, author = {Bhyravarapu, Sriram and Jana, Satyabrata and Kanesh, Lawqueen and Saurabh, Saket and Verma, Shaily}, booktitle = {International Workshop on Combinatorial Algorithms (IWOCA)}, keywords = {shailyverma year2023}, pages = {74&ndash;86}, title = {Parameterized Algorithms for Eccentricity Shortest Path Problem}, year = 2023 }

Cohen, Sarel; Fischbeck, Philipp; Friedrich, Tobias; Krejca, Martin S. The Common-Neighbors Metric is Noise-Robust and Reveals Substructures of Real-World NetworksPacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD) 2023: 67–79
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Real-world networks typically display a complex structure that is hard to explain by a single model. A common approach is to partition the edges of the network into disjoint simpler structures. An important property in this context is locality—incident vertices usually have many common neighbors. This allows to classify edges into two groups, based on the number of the common neighbors of their incident vertices. Formally, this is captured by the common-neighbors (CN) metric, which forms the basis of many metrics for detecting outlier edges. Such outliers can be interpreted as noise or as a substructure. We aim to understand how useful the metric is, and empirically analyze several scenarios. We randomly insert outlier edges into real-world and generated graphs with high locality, and measure the metric accuracy for partitioning the combined edges. In addition, we use the metric to decompose real-world networks, and measure properties of the partitions. Our results show that the CN metric is a very good classifier that can reliably detect noise up to extreme levels (\(83\%\) noisy edges). We also provide mathematically rigorous analyses on special random-graph models. Last, we find the CN metric consistently decomposes real-world networks into two graphs with very different structures.
@inproceedings{cohen2023commonneighbors, abstract = {Real-world networks typically display a complex structure that is hard to explain by a single model. A common approach is to partition the edges of the network into disjoint simpler structures. An important property in this context is locality—incident vertices usually have many common neighbors. This allows to classify edges into two groups, based on the number of the common neighbors of their incident vertices. Formally, this is captured by the common-neighbors (CN) metric, which forms the basis of many metrics for detecting outlier edges. Such outliers can be interpreted as noise or as a substructure. We aim to understand how useful the metric is, and empirically analyze several scenarios. We randomly insert outlier edges into real-world and generated graphs with high locality, and measure the metric accuracy for partitioning the combined edges. In addition, we use the metric to decompose real-world networks, and measure properties of the partitions. Our results show that the CN metric is a very good classifier that can reliably detect noise up to extreme levels (\(83\%\) noisy edges). We also provide mathematically rigorous analyses on special random-graph models. Last, we find the CN metric consistently decomposes real-world networks into two graphs with very different structures.}, author = {Cohen, Sarel and Fischbeck, Philipp and Friedrich, Tobias and Krejca, Martin S.}, booktitle = {Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD)}, keywords = {sarelcohen philippfischbeck martinskrejca tobiasfriedrich year2023 pakdd}, pages = {67&ndash;79}, title = {The Common-Neighbors Metric is Noise-Robust and Reveals Substructures of Real-World Networks}, year = 2023 }

Friedrich, Tobias; Gawendowicz, Hans; Lenzner, Pascal; Zahn, Arthur The Impact of Cooperation in Bilateral Network CreationACM Symposium on Principles of Distributed Computing (PODC) 2023
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Many real-world networks, like the Internet or social networks, are not the result of central design but instead the outcome of the interaction of local agents that selfishly optimize their individual utility. The well-known Network Creation Game by Fabrikant, Luthra, Maneva, Papadimitriou, and Shenker [PODC 2003] models this. There, agents corresponding to network nodes buy incident edges towards other agents for a price of \(\alpha > 0\) and simultaneously try to minimize their buying cost and their total hop distance. Since in many real-world networks, e.g., social networks, consent from both sides is required to establish and maintain a connection, Corbo and Parkes [PODC 2005] proposed a bilateral version of the Network Creation Game, in which mutual consent and payment are required in order to create edges. It is known that this cooperative version has a significantly higher Price of Anarchy compared to the unilateral version. On the first glance this is counter-intuitive, since cooperation should help to avoid socially bad states. However, in the bilateral version only a very restrictive form of cooperation is considered. We investigate this trade-off between the amount of cooperation and the Price of Anarchy by analyzing the bilateral version with respect to various degrees of cooperation among the agents. With this, we provide insights into what kind of cooperation is needed to ensure that socially good networks are created. As a first step in this direction, we focus on tree networks and present a collection of asymptotically tight bounds on the Price of Anarchy that precisely map the impact of cooperation. Most strikingly, we find that weak forms of cooperation already yield a significantly improved Price of Anarchy. In particular, the cooperation of coalitions of size 3 is enough to achieve constant bounds. Moreover, for general networks we show that enhanced cooperation yields close to optimal networks for a wide range of edge prices. Along the way, we disprove an old conjecture by Corbo and Parkes [PODC 2005].
@inproceedings{friedrich2023impact, abstract = {Many real-world networks, like the Internet or social networks, are not the result of central design but instead the outcome of the interaction of local agents that selfishly optimize their individual utility. The well-known Network Creation Game by Fabrikant, Luthra, Maneva, Papadimitriou, and Shenker [PODC 2003] models this. There, agents corresponding to network nodes buy incident edges towards other agents for a price of \(\alpha > 0\) and simultaneously try to minimize their buying cost and their total hop distance. Since in many real-world networks, e.g., social networks, consent from both sides is required to establish and maintain a connection, Corbo and Parkes [PODC 2005] proposed a bilateral version of the Network Creation Game, in which mutual consent and payment are required in order to create edges. It is known that this cooperative version has a significantly higher Price of Anarchy compared to the unilateral version. On the first glance this is counter-intuitive, since cooperation should help to avoid socially bad states. However, in the bilateral version only a very restrictive form of cooperation is considered. We investigate this trade-off between the amount of cooperation and the Price of Anarchy by analyzing the bilateral version with respect to various degrees of cooperation among the agents. With this, we provide insights into what kind of cooperation is needed to ensure that socially good networks are created. As a first step in this direction, we focus on tree networks and present a collection of asymptotically tight bounds on the Price of Anarchy that precisely map the impact of cooperation. Most strikingly, we find that weak forms of cooperation already yield a significantly improved Price of Anarchy. In particular, the cooperation of coalitions of size 3 is enough to achieve constant bounds. Moreover, for general networks we show that enhanced cooperation yields close to optimal networks for a wide range of edge prices. Along the way, we disprove an old conjecture by Corbo and Parkes [PODC 2005].}, author = {Friedrich, Tobias and Gawendowicz, Hans and Lenzner, Pascal and Zahn, Arthur}, booktitle = {ACM Symposium on Principles of Distributed Computing (PODC)}, keywords = {hansgawendowicz podc tobiasfriedrich year2023 pascallenzner}, title = {The Impact of Cooperation in Bilateral Network Creation}, year = 2023 }

Anand, Konrad; Göbel, Andreas; Pappik, Marcus; Perkins, Will Perfect Sampling for Hard Spheres from Strong Spatial MixingInternational Conference on Randomization and Computation (Random) 2023: 38:1–38:18
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
We provide a perfect sampling algorithm for the hard-sphere model on subsets of ℝd with expected running time linear in the volume under the assumption of strong spatial mixing. A large number of perfect and approximate sampling algorithms have been devised to sample from the hard-sphere model, and our perfect sampling algorithm is efficient for a range of parameters for which only efficient approximate samplers were previously known and is faster than these known approximate approaches. Our methods also extend to the more general setting of Gibbs point processes interacting via finite-range, repulsive potentials.
@inproceedings{anand2023perfect, abstract = {We provide a perfect sampling algorithm for the hard-sphere model on subsets of ℝd with expected running time linear in the volume under the assumption of strong spatial mixing. A large number of perfect and approximate sampling algorithms have been devised to sample from the hard-sphere model, and our perfect sampling algorithm is efficient for a range of parameters for which only efficient approximate samplers were previously known and is faster than these known approximate approaches. Our methods also extend to the more general setting of Gibbs point processes interacting via finite-range, repulsive potentials.}, author = {Anand, Konrad and Göbel, Andreas and Pappik, Marcus and Perkins, Will}, booktitle = {International Conference on Randomization and Computation (Random)}, keywords = {random sys:relevantfor:ae marcuspappik andreasgoebel tobiasfriedrich year2023}, pages = {38:1&ndash;38:18}, title = {Perfect Sampling for Hard Spheres from Strong Spatial Mixing}, year = 2023 }

Angrick, Sebastian; Bals, Ben; Casel, Katrin; Cohen, Sarel; Friedrich, Tobias; Hastrich, Niko; Hradilak, Theresa; Issac, Davis; Kißig, Otto; Schmidt, Jonas; Wendt, Leo Solving Directed Feedback Vertex Set by Iterative Reduction to Vertex CoverSymposium on Experimental Algorithms (SEA) 2023: 10:1–10:14
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
In the Directed Feedback Vertex Set (DFVS) problem, one is given a directed graph \(G = (V,E)\) and wants to find a minimum cardinality set \(S \subseteq V\) such that \(G-S\) is acyclic. DFVS is a fundamental problem in computer science and finds applications in areas such as deadlock detection. The problem was the subject of the 2022 PACE coding challenge. We develop a novel exact algorithm for the problem that is tailored to perform well on instances that are mostly bi-directed. For such instances, we adapt techniques from the well-researched vertex cover problem. Our core idea is an iterative reduction to vertex cover. To this end, we also develop a new reduction rule that reduces the number of not bi-directed edges. With the resulting algorithm, we were able to win third place in the exact track of the PACE challenge. We perform computational experiments and compare the running time to other exact algorithms, in particular to the winning algorithm in PACE. Our experiments show that we outpace the other algorithms on instances that have a low density of uni-directed edges.
@inproceedings{angrick_et_al:LIPIcs.SEA.2023.10, abstract = {In the Directed Feedback Vertex Set (DFVS) problem, one is given a directed graph \(G = (V,E)\) and wants to find a minimum cardinality set \(S \subseteq V\) such that \(G-S\) is acyclic. DFVS is a fundamental problem in computer science and finds applications in areas such as deadlock detection. The problem was the subject of the 2022 PACE coding challenge. We develop a novel exact algorithm for the problem that is tailored to perform well on instances that are mostly bi-directed. For such instances, we adapt techniques from the well-researched vertex cover problem. Our core idea is an iterative reduction to vertex cover. To this end, we also develop a new reduction rule that reduces the number of not bi-directed edges. With the resulting algorithm, we were able to win third place in the exact track of the PACE challenge. We perform computational experiments and compare the running time to other exact algorithms, in particular to the winning algorithm in PACE. Our experiments show that we outpace the other algorithms on instances that have a low density of uni-directed edges.}, address = {Dagstuhl, Germany}, annote = {Keywords: directed feedback vertex set, vertex cover, reduction rules}, author = {Angrick, Sebastian and Bals, Ben and Casel, Katrin and Cohen, Sarel and Friedrich, Tobias and Hastrich, Niko and Hradilak, Theresa and Issac, Davis and Kißig, Otto and Schmidt, Jonas and Wendt, Leo}, booktitle = {Symposium on Experimental Algorithms (SEA)}, keywords = {sarelcohen tobiasfriedrich year2023 sea}, pages = {10:1&ndash;10:14}, publisher = {Schloss Dagstuhl &ndash; Leibniz-Zentrum für Informatik}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, title = {Solving Directed Feedback Vertex Set by Iterative Reduction to Vertex Cover}, volume = 265, year = 2023 }

Fomin, Fedor V.; Golovach, Petr A.; Korhonen, Tuukka; Simonov, Kirill; Stamoulis Giannοs Fixed-Parameter Tractability of Maximum Colored Path and BeyondSymposium on Discrete Algorithms (SODA) 2023
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
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 \($2^p+\mathcal{O(k^2 log (q+k)) n^\mathcal{O w$\) time randomized algorithm for this problem.
@inproceedings{fomin2023fixedparameter, 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 Björklund, Husfeldt, and Taslaman&nbsp;[SODA&nbsp;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 $2^{p+\mathcal{O}(k^2 \log (q+k))} n^{\mathcal{O}} w$ time randomized algorithm for this problem.}, author = {Fomin, Fedor V. and Golovach, Petr A. and Korhonen, Tuukka and Simonov, Kirill and Stamoulis, Giannοs}, booktitle = {Symposium on Discrete Algorithms (SODA)}, keywords = {sys:relevantfor:ae kirillsimonov year2023 soda}, title = {Fixed-Parameter Tractability of Maximum Colored Path and Beyond}, year = 2023 }

Bläsius, Thomas; Friedrich, Tobias; Katzmann, Maximilian; Stephan, Daniel Strongly Hyperbolic Unit Disk GraphsSymposium Theoretical Aspects of Computer Science (STACS) 2023: 13:1–13:17
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The class of Euclidean unit disk graphs is one of the most fundamental and well-studied graph classes with underlying geometry. In this paper, we identify this class as a special case in the broader class of hyperbolic unit disk graphs and introduce strongly hyperbolic unit disk graphs as a natural counterpart to the Euclidean variant. In contrast to the grid-like structures exhibited by Euclidean unit disk graphs, strongly hyperbolic networks feature hierarchical structures, which are also observed in complex real-world networks. We investigate basic properties of strongly hyperbolic unit disk graphs, including adjacencies and the formation of cliques, and utilize the derived insights to demonstrate that the class is useful for the development and analysis of graph algorithms. Specifically, we develop a simple greedy routing scheme and analyze its performance on strongly hyperbolic unit disk graphs in order to prove that routing can be performed more efficiently on such networks than in general.
@inproceedings{blasius2023strongly, abstract = {The class of Euclidean unit disk graphs is one of the most fundamental and well-studied graph classes with underlying geometry. In this paper, we identify this class as a special case in the broader class of hyperbolic unit disk graphs and introduce strongly hyperbolic unit disk graphs as a natural counterpart to the Euclidean variant. In contrast to the grid-like structures exhibited by Euclidean unit disk graphs, strongly hyperbolic networks feature hierarchical structures, which are also observed in complex real-world networks. We investigate basic properties of strongly hyperbolic unit disk graphs, including adjacencies and the formation of cliques, and utilize the derived insights to demonstrate that the class is useful for the development and analysis of graph algorithms. Specifically, we develop a simple greedy routing scheme and analyze its performance on strongly hyperbolic unit disk graphs in order to prove that routing can be performed more efficiently on such networks than in general.}, author = {Bläsius, Thomas and Friedrich, Tobias and Katzmann, Maximilian and Stephan, Daniel}, booktitle = {Symposium Theoretical Aspects of Computer Science (STACS)}, keywords = {thomasblaesius stacs tobiasfriedrich danielstephan year2023 maximiliankatzmann}, pages = {13:1&ndash;13:17}, title = {Strongly Hyperbolic Unit Disk Graphs}, year = 2023 }

Friedrich, Tobias; Issac, Davis; Kumar, Nikhil; Mallek, Nadym; Zeif, Ziena Approximate Max-Flow Min-Multicut Theorem for Graphs of Bounded TreewidthSymposium Theory of Computing (STOC) 2023: 1325–1334
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
We prove an approximate max-multiflow min-multicut theorem for bounded treewidth graphs. In particular, we show the following: Given a treewidth-\(r\) graph, there exists a (fractional) multicommodity flow of value \(f\), and a multicut of capacity \(c\) such that \(f leq c leq \mathcal{O(\ln(r + 1)) \cdot f \) . It is well known that the multiflow-multicut gap on an \(r\)-vertex (constant degree) expander graph can be \(\Omega(ln r)\), and hence our result is tight up to constant factors. Our proof is constructive, and we also obtain a polynomial time \( \mathcal{O(ln(r + 1))\)-approximation algorithm for the minimum multicut problem on treewidth-r graphs. Our algorithm proceeds by rounding the optimal fractional solution to the natural linear programming relaxation of the multicut problem. We introduce novel modifications to the well-known region growing algorithm to facilitate the rounding while guaranteeing at most a logarithmic factor loss in the treewidth.
@inproceedings{friedrich2023approximate, abstract = {We prove an approximate max-multiflow min-multicut theorem for bounded treewidth graphs. In particular, we show the following: Given a treewidth-\(r\) graph, there exists a (fractional) multicommodity flow of value \(f\), and a multicut of capacity \(c\) such that \(f \leq c \leq \mathcal{O}(\ln(r + 1)) \cdot f \) . It is well known that the multiflow-multicut gap on an \(r\)-vertex (constant degree) expander graph can be \(\Omega(ln r)\), and hence our result is tight up to constant factors. Our proof is constructive, and we also obtain a polynomial time \( \mathcal{O}(ln(r + 1))\)-approximation algorithm for the minimum multicut problem on treewidth-r graphs. Our algorithm proceeds by rounding the optimal fractional solution to the natural linear programming relaxation of the multicut problem. We introduce novel modifications to the well-known region growing algorithm to facilitate the rounding while guaranteeing at most a logarithmic factor loss in the treewidth.}, author = {Friedrich, Tobias and Issac, Davis and Kumar, Nikhil and Mallek, Nadym and Zeif, Ziena}, booktitle = {Symposium Theory of Computing (STOC)}, keywords = {stoc zienazeif nikhilkumar davisissac tobiasfriedrich year2023 nadymmallek}, pages = {1325&ndash;1334}, title = {Approximate Max-Flow Min-Multicut Theorem for Graphs of Bounded Treewidth}, year = 2023 }

Bilò, Davide; Chechik, Shiri; Choudhary, Keerti; Cohen, Sarel; Friedrich, Tobias; Krogmann, Simon; Schirneck, Martin Approximate Distance Sensitivity Oracles in Subquadratic SpaceSymposium on Theory of Computing (STOC) 2023: 1396–1409
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An \(f\)-edge fault-tolerant distance sensitive oracle (\(f\)-DSO) with stretch \(\sigma\ge1\) is a data structure that preprocesses a given undirected, unweighted graph \(G\) with \(n\) vertices and \(m\) edges, and a positive integer \(f\). When queried with a pair of vertices \(s,t\) and a set \(F\) of at most \(f\) edges, it returns a \(\sigma\)-approximation of the \(s\)-\(t\)-distance in \(G-F\). We study \(f\)-DSOs that take subquadratic space. Thorup and Zwick [JACM 2015] showed that this is only possible for \(\sigma\geq3\). We present, for any constant \(f\geq1\) and \(\alpha\in(0,\frac{1}{2})\), and any \(\varepsilon>0\), an \(f\)-DSO with stretch \(3+\varepsilon\) that takes \(\tilde{O}(n^{2-\frac{\alpha}{f+1}}/\varepsilon)\cdot{}O(\log n/\varepsilon)^{f+1}\) space and has an \(O(n^\alpha/\varepsilon^2)\) query time. We also give an improved construction for graphs with diameter at most \(D\). For any constant \(k\), we devise an \(f\)-DSO with stretch \(2k-1\) that takes \(O(D^{f+o(1)}n^{1+1/k})\) space and has \(\tilde{O}(D^o(1)})\) query time, with a preprocessing time of \(O(D^{f+o(1)}mn^{1/k})\). Chechik, Cohen, Fiat, and Kaplan [SODA 2017] presented an \(f\)-DSO with stretch \(1{+}\varepsilon\) and preprocessing time \(\tilde{O}_\varepsilon(n^5)\), albeit with a super-quadratic space requirement. We show how to reduce their preprocessing time to \(O(mn^{2})\cdot{}O(\log n/\varepsilon)^{f}\).
@inproceedings{bilo2023approximate, abstract = {An \(f\)-edge fault-tolerant distance sensitive oracle (\(f\)-DSO) with stretch \(\sigma\ge1\) is a data structure that preprocesses a given undirected, unweighted graph \(G\) with \(n\) vertices and \(m\) edges, and a positive integer \(f\). When queried with a pair of vertices \(s,t\) and a set \(F\) of at most \(f\) edges, it returns a \(\sigma\)-approximation of the \(s\)-\(t\)-distance in \(G-F\). We study \(f\)-DSOs that take subquadratic space. Thorup and Zwick [JACM 2015] showed that this is only possible for \(\sigma\geq3\). We present, for any constant \(f\geq1\) and \(\alpha\in(0,\frac{1}{2})\), and any \(\varepsilon>0\), an \(f\)-DSO with stretch \(3+\varepsilon\) that takes \(\tilde{O}(n^{2-\frac{\alpha}{f+1}}/\varepsilon)\cdot{}O(\log n/\varepsilon)^{f+1}\) space and has an \(O(n^\alpha/\varepsilon^2)\) query time. We also give an improved construction for graphs with diameter at most \(D\). For any constant \(k\), we devise an \(f\)-DSO with stretch \(2k-1\) that takes \(O(D^{f+o(1)}n^{1+1/k})\) space and has \(\tilde{O}(D^{o(1)})\) query time, with a preprocessing time of \(O(D^{f+o(1)}mn^{1/k})\). Chechik, Cohen, Fiat, and Kaplan [SODA 2017] presented an \(f\)-DSO with stretch \(1{+}\varepsilon\) and preprocessing time \(\tilde{O}_\varepsilon(n^5)\), albeit with a super-quadratic space requirement. We show how to reduce their preprocessing time to \(O(mn^{2})\cdot{}O(\log n/\varepsilon)^{f}\).}, author = {Bilò, Davide and Chechik, Shiri and Choudhary, Keerti and Cohen, Sarel and Friedrich, Tobias and Krogmann, Simon and Schirneck, Martin}, booktitle = {Symposium on Theory of Computing (STOC)}, keywords = {sarelcohen stoc tobiasfriedrich year2023 simonkrogmann martinschirneck}, pages = {1396-1409}, title = {Approximate Distance Sensitivity Oracles in Subquadratic Space}, year = 2023 }

Baligács, Júlia; Disser, Yann; Soheil, Farehe; Weckbecker, David Tight Analysis of the Lazy Algorithm for Open Online Dial-a-RideWorkshop Algorithms and Data Structures (WADS) 2023: 43–64
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
In the open online dial-a-ride problem, a single server has to deliver transportation requests appearing over time in some metric space, subject to minimizing the completion time. We improve on the best known upper bounds on the competitive ratio on general metric spaces and on the half-line, for both the preemptive and non-preemptive version of the problem. We achieve this by revisiting the algorithm Lazy recently suggested in [WAOA, 2022] and giving an improved and tight analysis. More precisely, we show that it has competitive ratio 2.457 on general metric spaces and 2.366 on the half-line. This is the first upper bound that beats known lower bounds of 2.5 for schedule-based algorithms as well as the natural Replan algorithm.
@inproceedings{DBLP:conf/wads/BaligacsDSW23, abstract = {In the open online dial-a-ride problem, a single server has to deliver transportation requests appearing over time in some metric space, subject to minimizing the completion time. We improve on the best known upper bounds on the competitive ratio on general metric spaces and on the half-line, for both the preemptive and non-preemptive version of the problem. We achieve this by revisiting the algorithm Lazy recently suggested in [WAOA, 2022] and giving an improved and tight analysis. More precisely, we show that it has competitive ratio 2.457 on general metric spaces and 2.366 on the half-line. This is the first upper bound that beats known lower bounds of 2.5 for schedule-based algorithms as well as the natural Replan algorithm.}, author = {Balig{{á}}cs, J{{ú}}lia and Disser, Yann and Soheil, Farehe and Weckbecker, David}, booktitle = {Workshop Algorithms and Data Structures (WADS)}, keywords = {farehesoheil year2023}, pages = {43&ndash;64}, title = {Tight Analysis of the Lazy Algorithm for Open Online Dial-a-Ride}, year = 2023 }

Bandyapadhyay, Sayan; Fomin, Fedor V.; Inamdar, Tanmay; Panolan, Fahad; Simonov, Kirill Socially Fair Matching: Exact and Approximation AlgorithmsWorkshop on Algorithms and Data Structures (WADS) 2023: 79–92
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Matching problems are some of the most well-studied problems in graph theory and combinatorial optimization, with a variety of theoretical as well as practical motivations. However, in many applications of optimization problems, a ``solution'' corresponds to real-life decisions that have major impact on humans belonging to diverse groups defined by attributes such as gender, race, or ethnicity. Due to this motivation, the notion of \emph{algorithmic fairness has recently emerged to prominence. Depending on specific application, researchers have introduced several notions of fairness. In this paper, we study a problem called ``Socially Fair Matching'', which combines the traditional Minimum Weight Perfect Matching problem with the notion of social fairness that has been studied in clustering literature [Abbasi et al., and Ghadiri et al., FAccT, 2021]. In our problem, the input is an edge-weighted complete bipartite graph, where the bipartition represent two groups of entities. The goal is to find a perfect matching as well as an assignment that assigns the cost of each matched edge to one of its endpoints, such that the maximum of the total cost assigned to either of the two groups is minimized. Unlike Minimum Weight Perfect Matching, we show that Socially Fair Matching is weakly NP-hard. On the positive side, we design a deterministic PTAS for the problem when the edge weights are arbitrary. Furthermore, if the weights are integers and polynomial in the number of vertices, then we give a randomized polynomial-time algorithm that solves the problem exactly. Next, we show that this algorithm can be used to obtain a randomized FPTAS when the weights are arbitrary.
@inproceedings{bandyapadhyay2023socially, abstract = {Matching problems are some of the most well-studied problems in graph theory and combinatorial optimization, with a variety of theoretical as well as practical motivations. However, in many applications of optimization problems, a ``solution'' corresponds to real-life decisions that have major impact on humans belonging to diverse groups defined by attributes such as gender, race, or ethnicity. Due to this motivation, the notion of \emph{algorithmic fairness} has recently emerged to prominence. Depending on specific application, researchers have introduced several notions of fairness. In this paper, we study a problem called ``Socially Fair Matching'', which combines the traditional Minimum Weight Perfect Matching problem with the notion of social fairness that has been studied in clustering literature [Abbasi et al., and Ghadiri et al., FAccT, 2021]. In our problem, the input is an edge-weighted complete bipartite graph, where the bipartition represent two groups of entities. The goal is to find a perfect matching as well as an assignment that assigns the cost of each matched edge to one of its endpoints, such that the maximum of the total cost assigned to either of the two groups is minimized. Unlike Minimum Weight Perfect Matching, we show that Socially Fair Matching is weakly NP-hard. On the positive side, we design a deterministic PTAS for the problem when the edge weights are arbitrary. Furthermore, if the weights are integers and polynomial in the number of vertices, then we give a randomized polynomial-time algorithm that solves the problem exactly. Next, we show that this algorithm can be used to obtain a randomized FPTAS when the weights are arbitrary.}, author = {Bandyapadhyay, Sayan and Fomin, Fedor V. and Inamdar, Tanmay and Panolan, Fahad and Simonov, Kirill}, booktitle = {Workshop on Algorithms and Data Structures (WADS)}, keywords = {sys:relevantfor:ae kirillsimonov year2023 wads}, pages = {79&ndash;92}, title = {Socially Fair Matching: Exact and Approximation Algorithms}, year = 2023 }

Bilò, Davide; Choudhary, Keerti; Cohen, Sarel; Friedrich, Tobias; Krogmann, Simon; Schirneck, Martin Compact Distance Oracles with Large Sensitivity and Low StretchAlgorithms and Data Structures Symposium (WADS) 2023: 149–163
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
An \(f\)-edge fault-tolerant distance sensitive oracle (\(f\)-DSO) with stretch \(\sigma \geq 1\) is a data-structure that preprocesses an input graph \(G = (V,E)\). When queried with the triple \((s,t,F)\), where \(s, t \in V\) and \(F \subseteq E\) contains at most \(f\) edges of \(G\), the oracle returns an estimate \(\widehat{d_G-F(s,t)\) of the distance \(d_{G-F}(s,t)\) between \(s\) and \(t\) in the graph \(G-F\) such that \(d_{G-F}(s,t) leq \widehat{d_G-F(s,t) leq sigma cdot d_G-F(s,t)\). For any positive integer \(k \ge 2\) and any \(0 < \alpha < 1\), we present an \(f\)-DSO with sensitivity \(f = o(\log n/\log\log n)\), stretch \(2k-1\), space \(O(n^{1+\frac{1}{k+\alpha+o(1)})\), and an \(\widetildeO(n^1+\frac{1}{k - \frac{\alpha}{k(f+1)}})\) query time. Prior to our work, there were only three known \(f\)-DSOs with subquadratic space. The first one by Chechik et al. [Algorithmica 2012] has a stretch of \((8k-2)(f+1)\), depending on \(f\). Another approach is storing an \(f\)-edge fault-tolerant \((2k-1)\)-spanner of \(G\). The bottleneck is the large query time due to the size of any such spanner, which is \(\Omega(n^{1+1/k})\) under the Erdős girth conjecture. Bilò et al. [STOC 2023] gave a solution with stretch \(3+\varepsilon\), query time \(O(n^{\alpha})\) but space \(O(n^{2-\frac{\alpha}{f+1}})\), approaching the quadratic barrier for large sensitivity. In the realm of subquadratic space, our \(f\)-DSOs are the first ones that guarantee, at the same time, large sensitivity, low stretch, and non-trivial query time. To obtain our results, we use the approximate distance oracles of Thorup and Zwick [JACM 2005], and the derandomization of the \(f\)-DSO of Weimann and Yuster [TALG 2013] that was recently given by Karthik and Parter [SODA 2021].
@inproceedings{bilo2023compact, abstract = {An \(f\)-edge fault-tolerant distance sensitive oracle (\(f\)-DSO) with stretch \(\sigma \geq 1\) is a data-structure that preprocesses an input graph \(G = (V,E)\). When queried with the triple \((s,t,F)\), where \(s, t \in V\) and \(F \subseteq E\) contains at most \(f\) edges of \(G\), the oracle returns an estimate \(\widehat{d}_{G-F}(s,t)\) of the distance \(d_{G-F}(s,t)\) between \(s\) and \(t\) in the graph \(G-F\) such that \(d_{G-F}(s,t) \leq \widehat{d}_{G-F}(s,t) \leq \sigma \cdot d_{G-F}(s,t)\). For any positive integer \(k \ge 2\) and any \(0 < \alpha < 1\), we present an \(f\)-DSO with sensitivity \(f = o(\log n/\log\log n)\), stretch \(2k-1\), space \(O(n^{1+\frac{1}{k}+\alpha+o(1)})\), and an \(\widetilde{O}(n^{1+\frac{1}{k} - \frac{\alpha}{k(f+1)}})\) query time. Prior to our work, there were only three known \(f\)-DSOs with subquadratic space. The first one by Chechik et al. [Algorithmica 2012] has a stretch of \((8k-2)(f+1)\), depending on \(f\). Another approach is storing an \(f\)-edge fault-tolerant \((2k-1)\)-spanner of \(G\). The bottleneck is the large query time due to the size of any such spanner, which is \(\Omega(n^{1+1/k})\) under the Erdős girth conjecture. Bilò et al. [STOC 2023] gave a solution with stretch \(3+\varepsilon\), query time \(O(n^{\alpha})\) but space \(O(n^{2-\frac{\alpha}{f+1}})\), approaching the quadratic barrier for large sensitivity. In the realm of subquadratic space, our \(f\)-DSOs are the first ones that guarantee, at the same time, large sensitivity, low stretch, and non-trivial query time. To obtain our results, we use the approximate distance oracles of Thorup and Zwick [JACM 2005], and the derandomization of the \(f\)-DSO of Weimann and Yuster [TALG 2013] that was recently given by Karthik and Parter [SODA 2021].}, author = {Bilò, Davide and Choudhary, Keerti and Cohen, Sarel and Friedrich, Tobias and Krogmann, Simon and Schirneck, Martin}, booktitle = {Algorithms and Data Structures Symposium (WADS)}, keywords = {sarelcohen davidebilo tobiasfriedrich year2023 keertichoudhary simonkrogmann martinschirneck wads}, pages = {149-163}, title = {Compact Distance Oracles with Large Sensitivity and Low Stretch}, year = 2023 }

Bandyapadhyay, Sayan; Fomin, Fedor V.; Inamdar, Tanmay; Simonov, Kirill Proportionally Fair Matching with Multiple GroupsWorkshop on Graph-Theoretic Concepts in Computer Science (WG) 2023: 1–15
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
We study matching problems with the notion of proportional fairness. Proportional fairness is one of the most popular notions of group fairness where every group is represented up to an extent proportional to the final selection size. Matching with proportional fairness or more commonly, proportionally fair matching, was introduced in [Chierichetti et al., AISTATS, 2019]. In this problem, we are given a graph \($G$\) whose edges are colored with colors from a set \($C$\). The task is for given \($0\le \alpha \le \beta \le 1$\), to find a maximum \($(\alpha,\beta)$\)-balanced matching \($M$\) in \($G$\), that is a matching where for every color \($c\in C$\) the number of edges in \($M$\) of color \($c$\) is between \($\alpha|M|$\) and \($\beta |M|$\). Chierichetti et al. initiated the study of this problem with two colors and in the context of bipartite graphs only. However, in many practical applications, the number of colors---although often a small constant---is larger than two. In this work, we make the first step towards understanding the computational complexity of proportionally fair matching with more than two colors. We design exact and approximation algorithms achieving reasonable guarantees on the quality of the matching as well as on the time complexity, and our algorithms work in general graphs. Our algorithms are also supported by suitable hardness bounds.
@inproceedings{bandyapadhyay2023proportionally, abstract = {We study matching problems with the notion of proportional fairness. Proportional fairness is one of the most popular notions of group fairness where every group is represented up to an extent proportional to the final selection size. Matching with proportional fairness or more commonly, proportionally fair matching, was introduced in [Chierichetti et al., AISTATS, 2019]. In this problem, we are given a graph $G$ whose edges are colored with colors from a set $C$. The task is for given $0\le \alpha \le \beta \le 1$, to find a maximum $(\alpha,\beta)$-balanced matching $M$ in $G$, that is a matching where for every color $c\in C$ the number of edges in $M$ of color $c$ is between $\alpha|M|$ and $\beta |M|$. Chierichetti et al. initiated the study of this problem with two colors and in the context of bipartite graphs only. However, in many practical applications, the number of colors&mdash;although often a small constant&mdash;is larger than two. In this work, we make the first step towards understanding the computational complexity of proportionally fair matching with more than two colors. We design exact and approximation algorithms achieving reasonable guarantees on the quality of the matching as well as on the time complexity, and our algorithms work in general graphs. Our algorithms are also supported by suitable hardness bounds.}, author = {Bandyapadhyay, Sayan and Fomin, Fedor V. and Inamdar, Tanmay and Simonov, Kirill}, booktitle = {Workshop on Graph-Theoretic Concepts in Computer Science (WG)}, keywords = {sys:relevantfor:ae kirillsimonov year2023 wg}, pages = {1&ndash;15}, title = {Proportionally Fair Matching with Multiple Groups}, year = 2023 }

Casel, Katrin; Friedrich, Tobias; Issac, Davis; Niklanovits, Aikaterini; Zeif, Ziena Efficient Constructions for the Gyori-Lovasz Theorem on Almost Chordal GraphsWorkshop Graph-Theoretic Concepts in Computer Science (WG) 2023: 143–156
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
In the 1970s, GyHo}ri and Lovász showed that for a \(k\)-connected \(n\)-vertex graph, a given set of terminal vertices \(t_1, \dots, t_k\) and natural numbers \(n_1, \dots, n_k\) satisfying \(\sum_{i=1^k n_i = n\), a connected vertex partition \(S_1, \dots, S_k\) satisfying \(t_i \in S_i\) and \(|S_i| = n_i\) exists. However, polynomial algorithms to actually compute such partitions are known so far only for \(k \leq 4\). This motivates us to take a new approach and constrain this problem to particular graph classes instead of restricting the values of \(k\). More precisely, we consider \(k\)-connected chordal graphs and a broader class of graphs related to them. For the first class, we give an algorithm with \(\mathcal{O(n^2)\) running time that solves the problem exactly, and for the second, an algorithm with \(\mathcal{O(n^4)\) running time that deviates on at most one vertex from the required vertex partition sizes.
@inproceedings{casel2023efficient, abstract = {In the 1970s, Gy\H{o}ri and Lov{á}sz showed that for a \(k\)-connected \(n\)-vertex graph, a given set of terminal vertices \(t_1, \dots, t_k\) and natural numbers \(n_1, \dots, n_k\) satisfying \(\sum_{i=1}^{k} n_i = n\), a connected vertex partition \(S_1, \dots, S_k\) satisfying \(t_i \in S_i\) and \(|S_i| = n_i\) exists. However, polynomial algorithms to actually compute such partitions are known so far only for \(k \leq 4\). This motivates us to take a new approach and constrain this problem to particular graph classes instead of restricting the values of \(k\). More precisely, we consider \(k\)-connected chordal graphs and a broader class of graphs related to them. For the first class, we give an algorithm with \(\mathcal{O}(n^2)\) running time that solves the problem exactly, and for the second, an algorithm with \(\mathcal{O}(n^4)\) running time that deviates on at most one vertex from the required vertex partition sizes.}, author = {Casel, Katrin and Friedrich, Tobias and Issac, Davis and Niklanovits, Aikaterini and Zeif, Ziena}, booktitle = {Workshop Graph-Theoretic Concepts in Computer Science (WG)}, keywords = {sys:relevantfor:ae zienazeif katrincasel davisissac aikaterininiklanovits tobiasfriedrich year2023 wg}, pages = {143&ndash;156}, title = {Efficient Constructions for the Gyori-Lovasz Theorem on Almost Chordal Graphs}, year = 2023 }

Fomin, Fedor; Golovach, Petr; Sagunov, Danil; Simonov, Kirill Turán’s Theorem Through Algorithmic LensWorkshop on Graph-Theoretic Concepts in Computer Science (WG) 2023: 348–362
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
The fundamental theorem of Turán from Extremal Graph Theory determines the exact bound on the number of edges \($t_r(n)$\) in an \($n$\)-vertex graph that does not contain a clique of size \($r+1$\). We establish an interesting link between Extremal Graph Theory and Algorithms by providing a simple compression algorithm that in linear time reduces the problem of finding a clique of size \($\ell$\) in an \($n$\)-vertex graph \($G$\) with \($m ge t_r(n)-k$\) edges, where \($\ell\leq r+1$\), to the problem of finding a maximum clique in a graph on at most \($5k$\) vertices. This also gives us an algorithm deciding in time \($2.49^k\cdot(n + m)$\) whether \($G$\) has a clique of size \($\ell$\). As a byproduct of the new compression algorithm, we give an algorithm that in time \($2^\mathcal{O(td^2 ) \cdot n^2$\) decides whether a graph contains an independent set of size at least \($n/(d+1) +t$\). Here \($d$\) is the average vertex degree of the graph \($G$\). The multivariate complexity analysis based on ETH indicates that the asymptotical dependence on several parameters in the running times of our algorithms is tight.
@inproceedings{fomin2023turns, abstract = {The fundamental theorem of Tur{á}n from Extremal Graph Theory determines the exact bound on the number of edges $t_r(n)$ in an $n$-vertex graph that does not contain a clique of size $r+1$. We establish an interesting link between Extremal Graph Theory and Algorithms by providing a simple compression algorithm that in linear time reduces the problem of finding a clique of size $\ell$ in an $n$-vertex graph $G$ with $m \ge t_r(n)-k$ edges, where $\ell\leq r+1$, to the problem of finding a maximum clique in a graph on at most $5k$ vertices. This also gives us an algorithm deciding in time $2.49^{k}\cdot(n + m)$ whether $G$ has a clique of size $\ell$. As a byproduct of the new compression algorithm, we give an algorithm that in time $2^{\mathcal{O}(td^2 )} \cdot n^2$ decides whether a graph contains an independent set of size at least $n/(d+1) +t$. Here $d$ is the average vertex degree of the graph $G$. The multivariate complexity analysis based on ETH indicates that the asymptotical dependence on several parameters in the running times of our algorithms is tight.}, author = {Fomin, Fedor and Golovach, Petr and Sagunov, Danil and Simonov, Kirill}, booktitle = {Workshop on Graph-Theoretic Concepts in Computer Science (WG)}, keywords = {sys:relevantfor:ae kirillsimonov year2023 wg}, pages = {348&ndash;362}, title = {Turán’s Theorem Through Algorithmic Lens}, 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
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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 }

Derbisz, Jan; Kanesh, Lawqueen; Madathil, Jayakrishnan; Sahu, Abhishek; Saurabh, Saket; Verma, Shaily A Polynomial Kernel for Bipartite Permutation Vertex DeletionAlgorithmica 2022: 3246–3275
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In a permutation graph, vertices represent the elements of a permutation, and edges represent pairs of elements that are reversed by the permutation. In the sc Permutation Vertex Deletion problem, given an undirected graph \(G\) and an integer \(k\), the objective is to test whether there exists a vertex subset \(S subseteq V(G)\) such that \(|S| \leq k\) and \(G-S\) is a permutation graph. The parameterized complexity of Permutation Vertex Deletion is a well-known open problem. Bożyk et al. [IPEC 2020] initiated a study on this problem by requiring that \(G-S\) be a bipartite permutation graph (a permutation graph that is bipartite). They called this the Bipartite Permutation Vertex Deletion (BPVD) problem. They showed that the problem admits a factor 9-approximation algorithm as well as a fixed parameter tractable (FPT) algorithm running in time \(\mathcal{O(9^k |V(G)|^{9})\). Moreover, they posed the question whether BPVD admits a polynomial kernel. We resolve this question in the affirmative by designing a polynomial kernel for BPVD. In particular, we obtain the following: Given an instance \((G,k)\) of BPVD, in polynomial time we obtain an equivalent instance \((G',k')\) of BPVD such that \(k'\leq k\), and \(|V(G')|+|E(G')| leq k^\mathcal{O(1)}\).
@article{DBLP:journals/algorithmica/DerbiszKMSSV22, abstract = {In a permutation graph, vertices represent the elements of a permutation, and edges represent pairs of elements that are reversed by the permutation. In the {sc Permutation Vertex Deletion} problem, given an undirected graph \(G\) and an integer \(k\), the objective is to test whether there exists a vertex subset \(S \subseteq V(G)\) such that \(|S| \leq k\) and \(G-S\) is a permutation graph. The parameterized complexity of Permutation Vertex Deletion is a well-known open problem. Bożyk et al. [IPEC 2020] initiated a study on this problem by requiring that \(G-S\) be a bipartite permutation graph (a permutation graph that is bipartite). They called this the Bipartite Permutation Vertex Deletion (BPVD) problem. They showed that the problem admits a factor 9-approximation algorithm as well as a fixed parameter tractable (FPT) algorithm running in time \(\mathcal{O}(9^k |V(G)|^{9})\). Moreover, they posed the question whether BPVD admits a polynomial kernel. We resolve this question in the affirmative by designing a polynomial kernel for BPVD. In particular, we obtain the following: Given an instance \((G,k)\) of BPVD, in polynomial time we obtain an equivalent instance \((G',k')\) of BPVD such that \(k'\leq k\), and \(|V(G')|+|E(G')| \leq k^{\mathcal{O}(1)}\).}, author = {Derbisz, Jan and Kanesh, Lawqueen and Madathil, Jayakrishnan and Sahu, Abhishek and Saurabh, Saket and Verma, Shaily}, journal = {Algorithmica}, keywords = {shailyverma year2022}, pages = {3246&ndash;3275}, title = {A Polynomial Kernel for Bipartite Permutation Vertex Deletion}, 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
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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
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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 }

Verma, Shaily; Fu, Hung-Lin; Panda, B. S. Adjacent vertex distinguishing total coloring in split graphsDiscret. Math. 2022: 113061
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An adjacent vertex distinguishing (AVD)-total coloring of a graph \(G\) is a total coloring such that any two adjacent vertices \(u\) and \(v\) have the distinct set of colors, that is, \(C(u)neq C(v)\), where \(C(v)\) is the set of colors of the edges incident on \(v\) and the color of \(v\). The adjacent vertex distinguishing (AVD)-total chromatic number of a graph \(G\), \(\chi_a''(G)\) is the minimum integer \(k\) such that there exists an AVD-total coloring of \(G\) using \(k\) colors. It is known that \(\chi_a''(G)\geq \Delta+1\), where \(\Delta\) is the maximum degree of the graph. The AVD-total coloring conjecture states that for any graph \(G\), \(\chi_a''(G)\leq \Delta+3\). In this paper, we study the AVD-total coloring in split graphs. We prove the AVD-total coloring conjecture for split graphs and classify certain classes of split graphs according to their AVD-total chromatic number.
@article{DBLP:journals/dm/VermaFP22, abstract = {An adjacent vertex distinguishing (AVD)-total coloring of a graph \(G\) is a total coloring such that any two adjacent vertices \(u\) and \(v\) have the distinct set of colors, that is, \(C(u)\neq C(v)\), where \(C(v)\) is the set of colors of the edges incident on \(v\) and the color of \(v\). The adjacent vertex distinguishing (AVD)-total chromatic number of a graph \(G\), \(\chi_a''(G)\) is the minimum integer \(k\) such that there exists an AVD-total coloring of \(G\) using \(k\) colors. It is known that \(\chi_a''(G)\geq \Delta+1\), where \(\Delta\) is the maximum degree of the graph. The AVD-total coloring conjecture states that for any graph \(G\), \(\chi_a''(G)\leq \Delta+3\). In this paper, we study the AVD-total coloring in split graphs. We prove the AVD-total coloring conjecture for split graphs and classify certain classes of split graphs according to their AVD-total chromatic number.}, author = {Verma, Shaily and Fu, Hung-Lin and Panda, B. S.}, journal = {Discret. Math.}, keywords = {shailyverma year2022}, pages = 113061, title = {Adjacent vertex distinguishing total coloring in split graphs}, 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
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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
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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
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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
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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 ] [ 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
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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
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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
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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 = {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 }

Kontogiannis, Spyros; Machaira, Paraskevi-Maria-Malevi; Paraskevopoulos, Andreas; Zaroliagis, Christos REX: A Realistic Time-Dependent Model for Multimodal Public TransportAlgorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS) 2022: 12:1–12:16
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We present the non-FIFO time-dependent graph model with REalistic vehicle eXchange times (REX) for schedule-based multimodal public transport, along with a novel query algorithm called TRIP-based LAbel-correction propagation (TRIPLA) algorithm that efficiently solves the realistic earliest-arrival routing problem. The REX model possesses all strong features of previous time-dependent graph models without suffering from their deficiencies. It handles non-negligible exchanges from one vehicle to another, as well as supports non-FIFO instances which are typical in public transport, without compromising space efficiency. We conduct a thorough experimental evaluation with real-world data which demonstrates that TRIPLA significantly outperforms all state-of-the-art query algorithms for multimodal earliest-arrival routing in schedule-based public transport.
@inproceedings{noauthororeditor2022realistic, abstract = {We present the non-FIFO time-dependent graph model with REalistic vehicle eXchange times (REX) for schedule-based multimodal public transport, along with a novel query algorithm called TRIP-based LAbel-correction propagation (TRIPLA) algorithm that efficiently solves the realistic earliest-arrival routing problem. The REX model possesses all strong features of previous time-dependent graph models without suffering from their deficiencies. It handles non-negligible exchanges from one vehicle to another, as well as supports non-FIFO instances which are typical in public transport, without compromising space efficiency. We conduct a thorough experimental evaluation with real-world data which demonstrates that TRIPLA significantly outperforms all state-of-the-art query algorithms for multimodal earliest-arrival routing in schedule-based public transport.}, author = {Kontogiannis, Spyros and Machaira, Paraskevi-Maria-Malevi and Paraskevopoulos, Andreas and Zaroliagis, Christos}, booktitle = {Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS)}, keywords = {atmos sys:relevantfor:ae paraskevimachaira year2022}, pages = {12:1&ndash;12:16}, title = {REX: A Realistic Time-Dependent Model for Multimodal Public Transport}, 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: 242–254
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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}, pages = {242–254}, 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
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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
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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
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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
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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
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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 ] [ URL ] [ DOI ] [ 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 }

Mertzios, George B; Michail, Othon; Skretas, George; Spirakis, Paul G.; Theofilatos, Michail The Complexity of Growing a GraphInternational Symposium on Algorithms and Experiments for Wireless Sensor Networks 2022: 123–137
[ BibTeX ] [ DOI ] [ Download ]
 
@inproceedings{mertzios2022complexity, author = {Mertzios, George B and Michail, Othon and Skretas, George and Spirakis, Paul G. and Theofilatos, Michail}, booktitle = {International Symposium on Algorithms and Experiments for Wireless Sensor Networks}, keywords = {myown sys:relevantfor:ae year2022 georgeskretas}, pages = {123-137}, publisher = {Springer}, title = {The Complexity of Growing a Graph}, 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 }

Bhyravarapu, Sriram; Jana, Satyabrata; Panolan, Fahad; Saurabh, Saket; Verma, Shaily List Homomorphism: Beyond the Known BoundariesTheoretical Informatics: Latin American Symposium (LATIN) 2022 2022: 593–609
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Given two graphs \(G\) and \(H\), and a list \(L(u)V(H)\) associated with each \(uV(G)\), a list homomorphism from \(G\) to \(H\) is a mapping \(f:V(G)V(H)\) such that (i) for all \(uV(G)\), \(f(u) L(u)\), and (ii) for all \(u,vV(G)\), if \(uvE(G)\) then \(f(u)f(v)E(H)\). The List Homomorphism problem asks whether there exists a list homomorphism from \(G\) to \(H\). Enright, Stewart and Tardos SIAM J. Discret. Math., 2014 showed that the List Homomorphism problem can be solved in \( \mathcal{O(n^{k^2}-3k+4) \) time on graphs where every connected induced subgraph of \(G\) admits ``a multichain ordering'' that includes permutation graphs, biconvex graphs, and interval graphs, where \(n=|V(G)|\) and \(k=|V(H)|\). We prove that List Homomorphism parameterized by \(k\) even when \(G\) is a bipartite permutation graph is W1-hard. In fact, our reduction implies that it is not solvable in time \(n^o(k)\), unless the Exponential Time Hypothesis (ETH) fails. We complement this result with a matching upper bound and another positive result. We design a \(O(n^8k+3)\) time algorithm for List Homomorphism on bipartite graphs that admit a multichain ordering that includes the class of bipartite permutation graphs and biconvex graphs. Moreover, we show that for bipartite graph \(G\) that admits a multichain ordering, List Homomorphism is fixed parameter tractable when parameterized by \(k\) and the number of layers in the multichain ordering of \(G\). In addition, we study a variant of List Homomorphism called List Locally Surjective Homomorphism. We prove that List Locally Surjective Homomorphism parameterized by the number of vertices in \(H\) is wh, even when \(G\) is a chordal graph and \(H\) is a split graph.
@inproceedings{DBLP:conf/latin/BhyravarapuJP0V22, abstract = {Given two graphs \(G\) and \(H\), and a list \(L(u)V(H)\) associated with each \(uV(G)\), a list homomorphism from \(G\) to \(H\) is a mapping \(f:V(G)V(H)\) such that (i) for all \(uV(G)\), \(f(u) L(u)\), and (ii) for all \(u,vV(G)\), if \(uvE(G)\) then \(f(u)f(v)E(H)\). The List Homomorphism problem asks whether there exists a list homomorphism from \(G\) to \(H\). Enright, Stewart and Tardos SIAM J. Discret. Math., 2014 showed that the List Homomorphism problem can be solved in \( \mathcal{O}(n^{k^2}-3k+4) \) time on graphs where every connected induced subgraph of \(G\) admits ``a multichain ordering'' that includes permutation graphs, biconvex graphs, and interval graphs, where \(n=|V(G)|\) and \(k=|V(H)|\). We prove that List Homomorphism parameterized by \(k\) even when \(G\) is a bipartite permutation graph is W1-hard. In fact, our reduction implies that it is not solvable in time \(n^o(k)\), unless the Exponential Time Hypothesis (ETH) fails. We complement this result with a matching upper bound and another positive result. We design a \(O(n^8k+3)\) time algorithm for List Homomorphism on bipartite graphs that admit a multichain ordering that includes the class of bipartite permutation graphs and biconvex graphs. Moreover, we show that for bipartite graph \(G\) that admits a multichain ordering, List Homomorphism is fixed parameter tractable when parameterized by \(k\) and the number of layers in the multichain ordering of \(G\). In addition, we study a variant of List Homomorphism called List Locally Surjective Homomorphism. We prove that List Locally Surjective Homomorphism parameterized by the number of vertices in \(H\) is wh, even when \(G\) is a chordal graph and \(H\) is a split graph.}, author = {Bhyravarapu, Sriram and Jana, Satyabrata and Panolan, Fahad and Saurabh, Saket and Verma, Shaily}, booktitle = {Theoretical Informatics: Latin American Symposium (LATIN) 2022}, keywords = {shailyverma year2022}, pages = {593&ndash;609}, title = {List Homomorphism: Beyond the Known Boundaries}, year = 2022 }

Ramanujan, M. S.; Sahu, Abhishek; Saurabh, Saket; Verma, Shaily An Exact Algorithm for Knot-Free Vertex DeletionMathematical Foundations of Computer Science (MFCS) 2022: 78:1–78:15
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
The study of the Knot-Free Vertex Deletion problem emerges from its application in the resolution of deadlocks called knots, detected in a classical distributed computation model, that is, the OR-model. A strongly connected subgraph \(Q\) of a digraph \(D\) with at least two vertices is said to be a knot if there is no arc \((u,v)\) of \(D\) with \(u in V(Q)\) and \(v notin V(Q)\) (no-out neighbors of the vertices in \(Q\)). Given a directed graph \(D\), the Knot-Free Vertex Deletion problem asks to compute a minimum-size subset \(Ssubset V(D)\) such that \(D[V\setminus S]\) contains no knots. There is no exact algorithm known for the problem in the literature that is faster than the trivial \(\mathcal{O^\star(2^n)\) brute-force algorithm. In this paper, we obtain the first non-trivial upper bound for the problem by designing an exact algorithm running in time \(\mathcal{O^\star(1.576^n)\), where \(n\) is the size of the vertex set in \(D\).
@inproceedings{ramanujan2022exact, abstract = {The study of the Knot-Free Vertex Deletion problem emerges from its application in the resolution of deadlocks called knots, detected in a classical distributed computation model, that is, the OR-model. A strongly connected subgraph \(Q\) of a digraph \(D\) with at least two vertices is said to be a knot if there is no arc \((u,v)\) of \(D\) with \(u \in V(Q)\) and \(v \notin V(Q)\) (no-out neighbors of the vertices in \(Q\)). Given a directed graph \(D\), the Knot-Free Vertex Deletion problem asks to compute a minimum-size subset \(S\subset V(D)\) such that \(D[V\setminus S]\) contains no knots. There is no exact algorithm known for the problem in the literature that is faster than the trivial \(\mathcal{O}^\star(2^n)\) brute-force algorithm. In this paper, we obtain the first non-trivial upper bound for the problem by designing an exact algorithm running in time \(\mathcal{O}^\star(1.576^n)\), where \(n\) is the size of the vertex set in \(D\).}, author = {Ramanujan, M. S. and Sahu, Abhishek and Saurabh, Saket and Verma, Shaily}, booktitle = {Mathematical Foundations of Computer Science (MFCS)}, keywords = {sys:relevantfor:ae shailyverma mfcs year2022}, pages = {78:1&ndash;78:15}, title = {An Exact Algorithm for Knot-Free Vertex Deletion}, 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
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
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
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
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
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
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
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
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
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
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
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
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
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
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
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
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
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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 }

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 }

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 }

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 }

Aziz, Haris; Cseh, Agnes; Dickerson, John; McElfresh, Duncan Optimal Kidney Exchange with ImmunosuppressantsConference on Artificial Intelligence (AAAI) 2021: 21–29
[ Abstract