2019

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  Friedrich, Tobias; Göbel, Andreas; Neumann, Frank; Quinzan, Francesco; Rothenberger, Ralf Greedy Maximization of Functions with Bounded Curvature Under Partition Matroid Constraints. Conference on Artificial Intelligence (AAAI) 2019: 2272-2279
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  We investigate the performance of a deterministic GREEDY algorithm for the problem of maximizing functions under a partition matroid constraint. We consider non-monotone submodular functions and monotone subadditive functions. Even though constrained maximization problems of monotone submodular functions have been extensively studied, little is known about greedy maximization of non-monotone submodular functions or monotone subadditive functions. We give approximation guarantees for GREEDY on these problems, in terms of the curvature. We find that this simple heuristic yields a strong approximation guarantee on a broad class of functions. We discuss the applicability of our results to three real-world problems: Maximizing the determinant function of a positive semidefinite matrix, and related problems such as the maximum entropy sampling problem, the constrained maximum cut problem on directed graphs, and combinatorial auction games. We conclude that GREEDY is well-suited to approach these problems. Overall, we present evidence to support the idea that, when dealing with constrained maximization problems with bounded curvature, one needs not search for (approximate) monotonicity to get good approximate solutions.
  @inproceedings{AAAI19a, abstract = {We investigate the performance of a deterministic GREEDY algorithm for the problem of maximizing functions under a partition matroid constraint. We consider non-monotone submodular functions and monotone subadditive functions. Even though constrained maximization problems of monotone submodular functions have been extensively studied, little is known about greedy maximization of non-monotone submodular functions or monotone subadditive functions. We give approximation guarantees for GREEDY on these problems, in terms of the curvature. We find that this simple heuristic yields a strong approximation guarantee on a broad class of functions. We discuss the applicability of our results to three real-world problems: Maximizing the determinant function of a positive semidefinite matrix, and related problems such as the maximum entropy sampling problem, the constrained maximum cut problem on directed graphs, and combinatorial auction games. We conclude that GREEDY is well-suited to approach these problems. Overall, we present evidence to support the idea that, when dealing with constrained maximization problems with bounded curvature, one needs not search for (approximate) monotonicity to get good approximate solutions.}, author = {Friedrich, Tobias and Göbel, Andreas and Neumann, Frank and Quinzan, Francesco and Rothenberger, Ralf}, booktitle = {Conference on Artificial Intelligence (AAAI)}, keywords = {aaai andreasgoebel francescoquinzan frankneumann ralfrothenberger tobiasfriedrich year2019}, pages = {2272-2279}, title = {Greedy Maximization of Functions with Bounded Curvature Under Partition Matroid Constraints}, year = 2019 }
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  Roostapour, Vahid; Neumann, Aneta; Neumann, Frank; Friedrich, Tobias Pareto Optimization for Subset Selection with Dynamic Cost Constraints. Conference on Artificial Intelligence (AAAI) 2019: 2354-2361
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  In this paper, we consider subset selection problems for functions \(f\) with constraints where the constraint bound \(B\) changes over time. We point out that adaptive variants of greedy approaches commonly used in the area of submodular optimization are not able to maintain their approximation quality. Investigating the recently introduced POMC Pareto optimization approach, we show that this algorithm efficiently computes a \( phi= (\alpha_f/2)(1-\frac{1}{e^{\alpha_f}})\)-approximation, where \(\alpha_f\) is the submodularity ratio, for each possible constraint bound \(b \leq B\). Furthermore, we show that POMC is able to adapt its set of solutions quickly in the case that \(B\) increases. Our experimental investigations for the influence maximization in social networks show the advantage of POMC over generalized greedy algorithms.
  @inproceedings{AAAI19b, abstract = {In this paper, we consider subset selection problems for functions \(f\) with constraints where the constraint bound \(B\) changes over time. We point out that adaptive variants of greedy approaches commonly used in the area of submodular optimization are not able to maintain their approximation quality. Investigating the recently introduced POMC Pareto optimization approach, we show that this algorithm efficiently computes a \( \phi= (\alpha_f/2)(1-\frac{1}{e^{\alpha_f}})\)-approximation, where \(\alpha_f\) is the submodularity ratio, for each possible constraint bound \(b \leq B\). Furthermore, we show that POMC is able to adapt its set of solutions quickly in the case that \(B\) increases. Our experimental investigations for the influence maximization in social networks show the advantage of POMC over generalized greedy algorithms.}, author = {Roostapour, Vahid and Neumann, Aneta and Neumann, Frank and Friedrich, Tobias}, booktitle = {Conference on Artificial Intelligence (AAAI)}, keywords = {aaai anetaneumann frankneumann tobiasfriedrich vahidroostapour year2019}, pages = {2354-2361}, title = {Pareto Optimization for Subset Selection with Dynamic Cost Constraints}, year = 2019 }
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  Feldotto, Matthias; Lenzner, Pascal; Molitor, Louise; Skopalik, Alexander From Hotelling to Load Balancing: Approximation and the Principle of Minimum Differentiation. Autonomous Agents and Multiagent Systems (AAMAS) 2019: 1949-1951
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  Competing firms tend to select similar locations for their stores. This phenomenon, called the principle of minimum differentiation, was captured by Hotelling with a landmark model of spatial competition but is still the object of an ongoing scientific debate. Although consistently observed in practice, many more realistic variants of Hotelling's model fail to support minimum differentiation or do not have pure equilibria at all. In particular, it was recently proven for a generalized model which incorporates negative network externalities and which contains Hotelling's model and classical selfish load balancing as special cases, that the unique equilibria do not adhere to minimum differentiation. Furthermore, it was shown that for a significant parameter range pure equilibria do not exist. We derive a sharp contrast to these previous results by investigating Hotelling's model with negative network externalities from an entirely new angle: approximate pure subgame perfect equilibria. This approach allows us to prove analytically and via agent-based simulations that approximate equilibria having good approximation guarantees and that adhere to minimum differentiation exist for the full parameter range of the model. Moreover, we show that the obtained approximate equilibria have high social welfare.
  @inproceedings{feldotto2019hotelling, abstract = {Competing firms tend to select similar locations for their stores. This phenomenon, called the principle of minimum differentiation, was captured by Hotelling with a landmark model of spatial competition but is still the object of an ongoing scientific debate. Although consistently observed in practice, many more realistic variants of Hotelling's model fail to support minimum differentiation or do not have pure equilibria at all. In particular, it was recently proven for a generalized model which incorporates negative network externalities and which contains Hotelling's model and classical selfish load balancing as special cases, that the unique equilibria do not adhere to minimum differentiation. Furthermore, it was shown that for a significant parameter range pure equilibria do not exist. We derive a sharp contrast to these previous results by investigating Hotelling's model with negative network externalities from an entirely new angle: approximate pure subgame perfect equilibria. This approach allows us to prove analytically and via agent-based simulations that approximate equilibria having good approximation guarantees and that adhere to minimum differentiation exist for the full parameter range of the model. Moreover, we show that the obtained approximate equilibria have high social welfare.}, author = {Feldotto, Matthias and Lenzner, Pascal and Molitor, Louise and Skopalik, Alexander}, booktitle = {Autonomous Agents and Multiagent Systems (AAMAS)}, keywords = {aamas alexanderskopalik louisemolitor matthiasfeldotto pascallenzner year2019}, pages = {1949-1951}, title = {From Hotelling to Load Balancing: Approximation and the Principle of Minimum Differentiation}, year = 2019 }
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  Bläsius, Thomas; Friedrich, Tobias; Lischeid, Julius; Meeks, Kitty; Schirneck, Martin Efficiently Enumerating Hitting Sets of Hypergraphs Arising in Data Profiling. Algorithm Engineering and Experiments (ALENEX) 2019: 130-143
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  We devise an enumeration method for inclusion-wise minimal hitting sets in hypergraphs. It has delay \(O(m^{k^\ast+1} \cdot n^2)\) and uses linear space. Hereby, \(n\) is the number of vertices, \(m\) the number of hyperedges, and \(k^\ast\) the rank of the transversal hypergraph. In particular, on classes of hypergraphs for which the cardinality \(k^\ast\) of the largest minimal hitting set is bounded, the delay is polynomial. The algorithm solves the extension problem for minimal hitting sets as a subroutine. We show that the extension problem is W[3]-complete when parameterised by the cardinality of the set which is to be extended. For the subroutine, we give an algorithm that is optimal under the exponential time hypothesis. Despite these lower bounds, we provide empirical evidence showing that the enumeration outperforms the theoretical worst-case guarantee on hypergraphs arising in the profiling of relational databases, namely, in the detection of unique column combinations.
  @inproceedings{blasius2019efficiently, abstract = {We devise an enumeration method for inclusion-wise minimal hitting sets in hypergraphs. It has delay \(O(m^{k^\ast+1} \cdot n^2)\) and uses linear space. Hereby, \(n\) is the number of vertices, \(m\) the number of hyperedges, and \(k^\ast\) the rank of the transversal hypergraph. In particular, on classes of hypergraphs for which the cardinality \(k^\ast\) of the largest minimal hitting set is bounded, the delay is polynomial. The algorithm solves the extension problem for minimal hitting sets as a subroutine. We show that the extension problem is W[3]-complete when parameterised by the cardinality of the set which is to be extended. For the subroutine, we give an algorithm that is optimal under the exponential time hypothesis. Despite these lower bounds, we provide empirical evidence showing that the enumeration outperforms the theoretical worst-case guarantee on hypergraphs arising in the profiling of relational databases, namely, in the detection of unique column combinations.}, author = {Bläsius, Thomas and Friedrich, Tobias and Lischeid, Julius and Meeks, Kitty and Schirneck, Martin}, booktitle = {Algorithm Engineering and Experiments (ALENEX)}, keywords = {alenex juliuslischeid kittymeeks martinschirneck thomasblaesius tobiasfriedrich year2019}, pages = {130-143}, title = {Efficiently Enumerating Hitting Sets of Hypergraphs Arising in Data Profiling}, year = 2019 }
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  Fokina, Ekaterina; Kötzing, Timo; San Mauro, Luca Limit Learning Equivalence Structures. Algorithmic Learning Theory (ALT) 2019: 1-20
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  While most research in Gold-style learning focuses on learning formal languages, we consider the identification of computable structures, specifically equivalence structures. In our core model the learner gets more and more information about which pairs of elements of a structure are related and which are not. The aim of the learner is to find (an effective description of) the isomorphism type of the structure presented in the limit. In accordance with language learning we call this learning criterion InfEx-learning (explanatory learning from informant). We start with a discussion and separations of different variants of this learning criterion, including learning from text (where the only information provided is which elements are related, and not which elements are not related) and finite learning (where the first actual conjecture of the learner has to be correct). This gives first intuitions and examples for what (classes of) structures are learnable and which are not. Our main contribution is a complete characterization of the learnable classes of structures in terms of a combinatorial property of the classes. This property allows us to derive a bound of \(\mathbf{0''}\) on the computational complexity required to learn uniformly enumerable classes of structures. Finally, we show how learning classes of structures relates to learning classes of languages by mapping learning tasks for structures to equivalent learning tasks for languages.
  @inproceedings{fokina2019limit, abstract = {While most research in Gold-style learning focuses on learning formal languages, we consider the identification of computable structures, specifically equivalence structures. In our core model the learner gets more and more information about which pairs of elements of a structure are related and which are not. The aim of the learner is to find (an effective description of) the isomorphism type of the structure presented in the limit. In accordance with language learning we call this learning criterion InfEx-learning (explanatory learning from informant). We start with a discussion and separations of different variants of this learning criterion, including learning from text (where the only information provided is which elements are related, and not which elements are not related) and finite learning (where the first actual conjecture of the learner has to be correct). This gives first intuitions and examples for what (classes of) structures are learnable and which are not. Our main contribution is a complete characterization of the learnable classes of structures in terms of a combinatorial property of the classes. This property allows us to derive a bound of \(\mathbf{0''}\) on the computational complexity required to learn uniformly enumerable classes of structures. Finally, we show how learning classes of structures relates to learning classes of languages by mapping learning tasks for structures to equivalent learning tasks for languages.}, author = {Fokina, Ekaterina and Kötzing, Timo and San Mauro, Luca}, booktitle = {Algorithmic Learning Theory (ALT)}, keywords = {alt ekaterinafokina lucasanmauro timokoetzing year2019}, pages = {1-20}, title = {Limit Learning Equivalence Structures}, volume = 98, year = 2019 }
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  Casel, Katrin; Fernau, Henning; Khosravian Ghadikolaei, Mehdi; Monnot, Jerome; Sikora, Florian Extension of vertex cover and independent set in some classes of graphs and generalizations. International Conference on Algorithms and Complexity (CIAC) 2019: 124-136
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  We study extension variants of the classical problems Vertex Cover and Independent Set. Given a graph \(G = (V, E)\) and a vertex set \(U \subseteq V\), it is asked if there exists a minimal vertex cover (resp. maximal independent set) \(S\) with \(U \subseteq S\) (resp. \(U \supseteq S\)). Possibly contradicting intuition, these problems tend to be NP-complete, even in graph classes where the classical problem can be solved efficiently. Yet, we exhibit some graph classes where the extension variant remains polynomial-time solvable. We also study the parameterized complexity of theses problems, with parameter \(|U|\), as well as the optimality of simple exact algorithms under ETH. All these complexity considerations are also carried out in very restricted scenarios, be it degree or topological restrictions (bipartite, planar or chordal graphs). This also motivates presenting some explicit branching algorithms for degree-bounded instances. We further discuss the price of extension, measuring the distance of \(U\) to the closest set that can be extended, which results in natural optimization problems related to extension problems for which we discuss polynomial-time approximability.
  @inproceedings{casel2019extensionCIAC, abstract = {We study extension variants of the classical problems Vertex Cover and Independent Set. Given a graph \(G = (V, E)\) and a vertex set \(U \subseteq V\), it is asked if there exists a minimal vertex cover (resp. maximal independent set) \(S\) with \(U \subseteq S\) (resp. \(U \supseteq S\)). Possibly contradicting intuition, these problems tend to be NP-complete, even in graph classes where the classical problem can be solved efficiently. Yet, we exhibit some graph classes where the extension variant remains polynomial-time solvable. We also study the parameterized complexity of theses problems, with parameter \(|U|\), as well as the optimality of simple exact algorithms under ETH. All these complexity considerations are also carried out in very restricted scenarios, be it degree or topological restrictions (bipartite, planar or chordal graphs). This also motivates presenting some explicit branching algorithms for degree-bounded instances. We further discuss the price of extension, measuring the distance of \(U\) to the closest set that can be extended, which results in natural optimization problems related to extension problems for which we discuss polynomial-time approximability.}, author = {Casel, Katrin and Fernau, Henning and Khosravian Ghadikolaei, Mehdi and Monnot, Jerome and Sikora, Florian}, booktitle = {International Conference on Algorithms and Complexity (CIAC)}, keywords = {ciac katrincasel year2019}, pages = {124-136}, title = {Extension of vertex cover and independent set in some classes of graphs and generalizations}, year = 2019 }
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  Bläsius, Thomas; Friedrich, Tobias; Katzmann, Maximilian; Meyer, Ulrich; Penschuck, Manuel; Weyand, Christopher Efficiently Generating Geometric Inhomogeneous and Hyperbolic Random Graphs. European Symposium on Algorithms (ESA) 2019: 21:2-21:14

  EATCS Best Paper Award
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  Hyperbolic random graphs (HRG) and geometric inhomogeneous random graphs (GIRG) are two similar generative network models that were designed to resemble complex real world networks. In particular, they have a power-law degree distribution with controllable exponent \(\beta\), and high clustering that can be controlled via the temperature \(T\). We present the first implementation of an efficient GIRG generator running in expected linear time. Besides varying temperatures, it also supports underlying geometries of higher dimensions. It is capable of generating graphs with ten million edges in under a second on commodity hardware. The algorithm can be adapted to HRGs. Our resulting implementation is the fastest sequential HRG generator, despite the fact that we support non-zero temperatures. Though non-zero temperatures are crucial for many applications, most existing generators are restricted to \(T = 0\). We also support parallelization, although this is not the focus of this paper. Moreover, we note that our generators draw from the correct probability distribution, i.e., they involve no approximation. Besides the generators themselves, we also provide an efficient algorithm to determine the non-trivial dependency between the average degree of the resulting graph and the input parameters of the GIRG model. This makes it possible to specify \(\bar{d}\) as input and obtain a graph with expected average degree \(\bar{d}\). Moreover, we investigate the differences between HRGs and GIRGs, shedding new light on the nature of the relation between the two models. Although HRGs represent, in a certain sense, a special case of the GIRG model, we find that a straight-forward inclusion does not hold in practice. However, the difference is negligible for most use cases.
  @inproceedings{blaesius2019efficiently, abstract = {Hyperbolic random graphs (HRG) and geometric inhomogeneous random graphs (GIRG) are two similar generative network models that were designed to resemble complex real world networks. In particular, they have a power-law degree distribution with controllable exponent \(\beta\), and high clustering that can be controlled via the temperature \(T\). We present the first implementation of an efficient GIRG generator running in expected linear time. Besides varying temperatures, it also supports underlying geometries of higher dimensions. It is capable of generating graphs with ten million edges in under a second on commodity hardware. The algorithm can be adapted to HRGs. Our resulting implementation is the fastest sequential HRG generator, despite the fact that we support non-zero temperatures. Though non-zero temperatures are crucial for many applications, most existing generators are restricted to \(T = 0\). We also support parallelization, although this is not the focus of this paper. Moreover, we note that our generators draw from the correct probability distribution, i.e., they involve no approximation. Besides the generators themselves, we also provide an efficient algorithm to determine the non-trivial dependency between the average degree of the resulting graph and the input parameters of the GIRG model. This makes it possible to specify \(\bar{d}\) as input and obtain a graph with expected average degree \(\bar{d}\). Moreover, we investigate the differences between HRGs and GIRGs, shedding new light on the nature of the relation between the two models. Although HRGs represent, in a certain sense, a special case of the GIRG model, we find that a straight-forward inclusion does not hold in practice. However, the difference is negligible for most use cases.}, author = {Bläsius, Thomas and Friedrich, Tobias and Katzmann, Maximilian and Meyer, Ulrich and Penschuck, Manuel and Weyand, Christopher}, booktitle = {European Symposium on Algorithms (ESA)}, keywords = {christopherweyand esa hyperbolic_generation manuelpenschuck maximiliankatzmann thomasblaesius tobiasfriedrich ulrichmeyer year2019}, note = {EATCS Best Paper Award}, pages = {21:2-21:14}, title = {Efficiently Generating Geometric Inhomogeneous and Hyperbolic Random Graphs}, year = 2019 }
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  Casel, Katrin; Fernau, Henning; Khosravian Ghadikolaei, Mehdi; Monnot, Jerome; Sikora, Florian Extension of some edge graph problems: standard and parameterized complexity. Fundamentals of Computation Theory (FCT) 2019: 185-200
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  We consider extension variants of some edge optimization problems in graphs containing the classical Edge Cover, Matching, and Edge Dominating Set problems. Given a graph \(G=(V,E)\) and an edge set \(U \subseteq E\), it is asked whether there exists an inclusion-wise minimal (resp., maximal) feasible solution \(E'\) which satisfies a given property, for instance, being an edge dominating set (resp., a matching) and containing the forced edge set \(U\) (resp., avoiding any edges from the forbidden edge set \(E U\)). We present hardness results for these problems, for restricted instances such as bipartite or planar graphs. We counter-balance these negative results with parameterized complexity results. We also consider the price of extension, a natural optimization problem variant of extension problems, leading to some approximation results.
  @inproceedings{casel2019extensionFCT, abstract = {We consider extension variants of some edge optimization problems in graphs containing the classical Edge Cover, Matching, and Edge Dominating Set problems. Given a graph \(G=(V,E)\) and an edge set \(U \subseteq E\), it is asked whether there exists an inclusion-wise minimal (resp., maximal) feasible solution \(E'\) which satisfies a given property, for instance, being an edge dominating set (resp., a matching) and containing the forced edge set \(U\) (resp., avoiding any edges from the forbidden edge set \(E U\)). We present hardness results for these problems, for restricted instances such as bipartite or planar graphs. We counter-balance these negative results with parameterized complexity results. We also consider the price of extension, a natural optimization problem variant of extension problems, leading to some approximation results.}, author = {Casel, Katrin and Fernau, Henning and Khosravian Ghadikolaei, Mehdi and Monnot, Jerome and Sikora, Florian}, booktitle = {Fundamentals of Computation Theory (FCT)}, keywords = {fct katrincasel year2019}, pages = {185-200}, title = {Extension of some edge graph problems: standard and parameterized complexity}, year = 2019 }
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  Doerr, Benjamin; Kötzing, Timo Multiplicative Up-Drift. Genetic and Evolutionary Computation Conference (GECCO) 2019
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  Drift analysis aims at translating the expected progress of an evo- lutionary algorithm (or more generally, a random process) into a probabilistic guarantee on its run time (hitting time). So far, drift arguments have been successfully employed in the rigorous analy- sis of evolutionary algorithms, however, only for the situation that the progress is constant or becomes weaker when approaching the target. Motivated by questions like how fast fit individuals take over a population, we analyze random processes exhibiting a multiplica- tive growth in expectation. We prove a drift theorem translating this expected progress into a hitting time. This drift theorem gives a sim- ple and insightful proof of the level-based theorem first proposed by Lehre (2011). Our version of this theorem has, for the first time, the best-possible linear dependence on the growth parameter \(\delta\) (the previous-best was quadratic). This gives immediately stronger run time guarantees for a number of applications.
  @inproceedings{doerr2019multiplicative, abstract = {Drift analysis aims at translating the expected progress of an evo- lutionary algorithm (or more generally, a random process) into a probabilistic guarantee on its run time (hitting time). So far, drift arguments have been successfully employed in the rigorous analy- sis of evolutionary algorithms, however, only for the situation that the progress is constant or becomes weaker when approaching the target. Motivated by questions like how fast fit individuals take over a population, we analyze random processes exhibiting a multiplica- tive growth in expectation. We prove a drift theorem translating this expected progress into a hitting time. This drift theorem gives a sim- ple and insightful proof of the level-based theorem first proposed by Lehre (2011). Our version of this theorem has, for the first time, the best-possible linear dependence on the growth parameter \(\delta\) (the previous-best was quadratic). This gives immediately stronger run time guarantees for a number of applications.}, author = {Doerr, Benjamin and Kötzing, Timo}, booktitle = {Genetic and Evolutionary Computation Conference (GECCO)}, keywords = {benjamindoerr gecco timokoetzing year2019}, title = {Multiplicative Up-Drift}, year = 2019 }
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  Friedrich, Tobias; Rothenberger, Ralf The Satisfiability Threshold for Non-Uniform Random 2-SAT. International Colloquium on Automata, Languages and Programming (ICALP) 2019: 61:1-61:14
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  Propositional satisfiability (SAT) is one of the most fundamental problems in computer science. Its worst-case hardness lies at the core of computational complexity theory, for example in the form of NP-hardness and the (Strong) Exponential Time Hypothesis. In practice however, SAT instances can often be solved efficiently. This contradicting behavior has spawned interest in the average-case analysis of SAT and has triggered the development of sophisticated rigorous and non-rigorous techniques for analyzing random structures. Despite a long line of research and substantial progress, most theoretical work on random SAT assumes a uniform distribution on the variables. In contrast, real-world instances often exhibit large fluctuations in variable occurrence. This can be modeled by a non-uniform distribution of the variables, which can result in distributions closer to industrial SAT instances. We study satisfiability thresholds of non-uniform random 2-SAT with n variables and m clauses and with an arbitrary probability distribution \((p_i)_{i \in [n]}\) with \(p_1 \geq p_2 \geq \dots \geq p_n > 0\) over the n variables. We show for \(p_1^2 = \Theta(\sum_{i=1}^n p_i^2)\) that the asymptotic satisfiability threshold is at \(m = \Theta((1− \sum_{i=1}^n p_i^2) / (p_1 cdot (\sum_{i=2}^n p_i^2)^{1/2}))\) and that it is coarse. For \(p_1^2 = o( \sum_{i=1}^n p_i^2)\) we show that there is a sharp satisfiability threshold at \(m = (\sum_{i=1}^n p_i^2)^{−1}\). This result generalizes the seminal works by Chvatal and Reed [FOCS 1992] and by Goerdt [JCSS 1996].
  @inproceedings{friedrich2019satisfiabilityICALP, abstract = {Propositional satisfiability (SAT) is one of the most fundamental problems in computer science. Its worst-case hardness lies at the core of computational complexity theory, for example in the form of NP-hardness and the (Strong) Exponential Time Hypothesis. In practice however, SAT instances can often be solved efficiently. This contradicting behavior has spawned interest in the average-case analysis of SAT and has triggered the development of sophisticated rigorous and non-rigorous techniques for analyzing random structures. Despite a long line of research and substantial progress, most theoretical work on random SAT assumes a uniform distribution on the variables. In contrast, real-world instances often exhibit large fluctuations in variable occurrence. This can be modeled by a non-uniform distribution of the variables, which can result in distributions closer to industrial SAT instances. We study satisfiability thresholds of non-uniform random 2-SAT with n variables and m clauses and with an arbitrary probability distribution \((p_i)_{i \in [n]}\) with \(p_1 \geq p_2 \geq \dots \geq p_n > 0\) over the n variables. We show for \(p_1^2 = \Theta(\sum_{i=1}^n p_i^2)\) that the asymptotic satisfiability threshold is at \(m = \Theta((1− \sum_{i=1}^n p_i^2) / (p_1 \cdot (\sum_{i=2}^n p_i^2)^{1/2}))\) and that it is coarse. For \(p_1^2 = o( \sum_{i=1}^n p_i^2)\) we show that there is a sharp satisfiability threshold at \(m = (\sum_{i=1}^n p_i^2)^{−1}\). This result generalizes the seminal works by Chvatal and Reed [FOCS 1992] and by Goerdt [JCSS 1996].}, author = {Friedrich, Tobias and Rothenberger, Ralf}, booktitle = {International Colloquium on Automata, Languages and Programming (ICALP)}, keywords = {icalp ralfrothenberger scalefree_sat tobiasfriedrich year2019}, pages = {61:1-61:14}, title = {The Satisfiability Threshold for Non-Uniform Random 2-SAT}, year = 2019 }
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  Casel, Katrin; Day, Joel D.; Fleischmann, Pamela; Kociumaka, Tomasz; Manea, Florin; Schmid, Markus L. Graph and String Parameters: Connections Between Pathwidth, Cutwidth and the Locality Number. International Colloquium on Automata, Languages and Programming (ICALP) 2019: 109:1-109:16
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  We investigate the locality number, a recently introduced structural parameter for strings (with applications in pattern matching with variables), and its connection to two important graph-parameters, cutwidth and pathwidth. These connections allow us to show that computing the locality number is NP-hard but fixed parameter tractable (when the locality number or the alphabet size is treated as a parameter), and can be approximated with ratio \(O(\sqrt{\log opt} \log n)\). As a by-product, we also relate cutwidth via the locality number to pathwidth, which is of independent interest, since it improves the currently best known approximation algorithm for cutwidth. In addition to these main results, we also consider the possibility of greedy-based approximation algorithms for the locality number.
  @inproceedings{casel2019graph, abstract = {We investigate the locality number, a recently introduced structural parameter for strings (with applications in pattern matching with variables), and its connection to two important graph-parameters, cutwidth and pathwidth. These connections allow us to show that computing the locality number is NP-hard but fixed parameter tractable (when the locality number or the alphabet size is treated as a parameter), and can be approximated with ratio \(O(\sqrt{\log opt} \log n)\). As a by-product, we also relate cutwidth via the locality number to pathwidth, which is of independent interest, since it improves the currently best known approximation algorithm for cutwidth. In addition to these main results, we also consider the possibility of greedy-based approximation algorithms for the locality number.}, author = {Casel, Katrin and Day, Joel D. and Fleischmann, Pamela and Kociumaka, Tomasz and Manea, Florin and Schmid, Markus L.}, booktitle = {International Colloquium on Automata, Languages and Programming (ICALP)}, keywords = {icalp katrincasel year2019}, pages = {109:1-109:16}, title = {Graph and String Parameters: Connections Between Pathwidth, Cutwidth and the Locality Number}, year = 2019 }
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  Peters, Jannik; Stephan, Daniel; Amon, Isabel; Gawendowicz, Hans; Lischeid, Julius; Salabarria, Julius; Umland, Jonas; Werner, Felix; Krejca, Martin S.; Rothenberger, Ralf; Kötzing, Timo; Friedrich, Tobias Mixed Integer Programming versus Evolutionary Computation for Optimizing a Hard Real-World Staff Assignment Problem. International Conference on Automated Planning and Scheduling (ICAPS) 2019: 541-554
  [ Abstract ] [ BibTeX ] [ URL ] [ Download ]
   
  Assigning staff to engagements according to hard constraints while optimizing several objectives is a task encountered by many companies on a regular basis. Simplified versions of such assignment problems are NP-hard. Despite this, a typical approach to solving them consists of formulating them as mixed integer programming (MIP) problems and using a state-of-the-art solver to get solutions that closely approximate the optimum. In this paper, we consider a complex real-world staff assignment problem encountered by the professional service company KPMG, with the goal of finding an algorithm that solves it faster and with a better solution than a commercial MIP solver. We follow the evolutionary algorithm (EA) metaheuristic and design a search heuristic which iteratively improves a solution using domain-specific mutation operators. Furthermore, we use a flow algorithm to optimally solve a subproblem, which tremendously reduces the search space for the EA. For our real-world instance of the assignment problem, given the same total time budget of \(100\) hours, a parallel EA approach finds a solution that is only \(1.7\)% away from an upper bound for the (unknown) optimum within under five hours, while the MIP solver Gurobi still has a gap of \(10.5\) %.
  @inproceedings{peters2019mixed, abstract = {Assigning staff to engagements according to hard constraints while optimizing several objectives is a task encountered by many companies on a regular basis. Simplified versions of such assignment problems are NP-hard. Despite this, a typical approach to solving them consists of formulating them as mixed integer programming (MIP) problems and using a state-of-the-art solver to get solutions that closely approximate the optimum. In this paper, we consider a complex real-world staff assignment problem encountered by the professional service company KPMG, with the goal of finding an algorithm that solves it faster and with a better solution than a commercial MIP solver. We follow the evolutionary algorithm (EA) metaheuristic and design a search heuristic which iteratively improves a solution using domain-specific mutation operators. Furthermore, we use a flow algorithm to optimally solve a subproblem, which tremendously reduces the search space for the EA. For our real-world instance of the assignment problem, given the same total time budget of \(100\) hours, a parallel EA approach finds a solution that is only \(1.7\)\% away from an upper bound for the (unknown) optimum within under five hours, while the MIP solver Gurobi still has a gap of \(10.5\) \%.}, author = {Peters, Jannik and Stephan, Daniel and Amon, Isabel and Gawendowicz, Hans and Lischeid, Julius and Salabarria, Julius and Umland, Jonas and Werner, Felix and Krejca, Martin S. and Rothenberger, Ralf and Kötzing, Timo and Friedrich, Tobias}, booktitle = {International Conference on Automated Planning and Scheduling (ICAPS)}, keywords = {danielstephan felixwerner hansgawendowicz icaps isabelamon jannikpeters jonasumland juliuslischeid lennartsalabarria martinskrejca ralfrothenberger timokoetzing tobiasfriedrich year2019}, pages = {541-554}, title = {Mixed Integer Programming versus Evolutionary Computation for Optimizing a Hard Real-World Staff Assignment Problem}, year = 2019 }
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  Friedrich, Tobias; Rothenberger, Ralf Sharpness of the Satisfiability Threshold for Non-Uniform Random k-SAT. International Joint Conference on Artificial Intelligence (IJCAI) 2019: 6151-6155

  Extended abstract
  [ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
   
  We study non-uniform random k-SAT on n variables with an arbitrary probability distribution p on the variable occurrences. The number \(t = t(n)\) of randomly drawn clauses at which random formulas go from asymptotically almost surely (a.a.s.) satisfiable to a.a.s. unsatisfiable is called the satisfiability threshold. Such a threshold is called sharp if it approaches a step function as n increases. We show that a threshold t(n) for random k-SAT with an ensemble \((p_n)_{n\in\mathbb{N}}\) of arbitrary probability distributions on the variable occurrences is sharp if \(\|p\|_2^2 = O_n(t^{-2/k})\) and \(\|p\|_infty = o_n(t^{-k/(2k-1)} \log^{-(k-1)/(2k-1)}(t))\). This result generalizes Friedgut’s sharpness result from uniform to non-uniform random k-SAT and implies sharpness for thresholds of a wide range of random k-SAT models with heterogeneous probability distributions, for example such models where the variable probabilities follow a power-law distribution.
  @inproceedings{friedrich2019satisfiabilityIJCAI, abstract = {We study non-uniform random k-SAT on n variables with an arbitrary probability distribution p on the variable occurrences. The number \(t = t(n)\) of randomly drawn clauses at which random formulas go from asymptotically almost surely (a.a.s.) satisfiable to a.a.s. unsatisfiable is called the satisfiability threshold. Such a threshold is called sharp if it approaches a step function as n increases. We show that a threshold t(n) for random k-SAT with an ensemble \((p_n)_{n\in\mathbb{N}}\) of arbitrary probability distributions on the variable occurrences is sharp if \(\|p\|_2^2 = O_n(t^{-2/k})\) and \(\|p\|_\infty = o_n(t^{-k/(2k-1)} \log^{-(k-1)/(2k-1)}(t))\). This result generalizes Friedgut’s sharpness result from uniform to non-uniform random k-SAT and implies sharpness for thresholds of a wide range of random k-SAT models with heterogeneous probability distributions, for example such models where the variable probabilities follow a power-law distribution.}, author = {Friedrich, Tobias and Rothenberger, Ralf}, booktitle = {International Joint Conference on Artificial Intelligence (IJCAI)}, keywords = {ijcai ralfrothenberger scalefree_sat tobiasfriedrich year2019}, note = {Extended abstract}, pages = {6151-6155}, title = {Sharpness of the Satisfiability Threshold for Non-Uniform Random k-SAT.}, year = 2019 }
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  Gao, Ziyuan; Jain, Sanjay; Khoussainov, Bakhadyr; Li, Wei; Melnikov, Alexander; Seidel, Karen; Stephan, Frank Random Subgroups of Rationals. International Symposium on Mathematical Foundations of Computer Science (MFCS) 2019: 25:1-25:14
  [ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
   
  This paper introduces and studies a notion of algorithmic randomness for subgroups of rationals. Given a randomly generated additive subgroup \((G,+)\) of rationals, two main questions are addressed: first, what are the model-theoretic and recursion-theoretic properties of \((G,+)\); second, what learnability properties can one extract from \(G\) and its subclass of finitely generated subgroups? For the first question, it is shown that the theory of \((G,+)\) coincides with that of the additive group of integers and is therefore decidable; furthermore, while the word problem for \(G\) with respect to any generating sequence for \(G\) is not even semi-decidable, one can build a generating sequence \(\beta\) such that the word problem for \(G\) with respect to \(\beta\) is co-recursively enumerable (assuming that the set of generators of \(G\) is limit-recursive). In regard to the second question, it is proven that there is a generating sequence \(\beta\) for \(G\) such that every non-trivial finitely generated subgroup of \(G\) is recursively enumerable and the class of all such subgroups of \(G\) is behaviourally correctly learnable, that is, every non-trivial finitely generated subgroup can be semantically identified in the limit (again assuming that the set of generators of \(G\) is limit-recursive). On the other hand, the class of non-trivial finitely generated subgroups of \(G\) cannot be syntactically identified in the limit with respect to any generating sequence for \(G\). The present work thus contributes to a recent line of research studying algorithmically random infinite structures and uncovers an interesting connection between the arithmetical complexity of the set of generators of a randomly generated subgroup of rationals and the learnability of its finitely generated subgroups.
  @inproceedings{gao_et_al:LIPIcs:2019:10969, abstract = {This paper introduces and studies a notion of algorithmic randomness for subgroups of rationals. Given a randomly generated additive subgroup \((G,+)\) of rationals, two main questions are addressed: first, what are the model-theoretic and recursion-theoretic properties of \((G,+)\); second, what learnability properties can one extract from \(G\) and its subclass of finitely generated subgroups? For the first question, it is shown that the theory of \((G,+)\) coincides with that of the additive group of integers and is therefore decidable; furthermore, while the word problem for \(G\) with respect to any generating sequence for \(G\) is not even semi-decidable, one can build a generating sequence \(\beta\) such that the word problem for \(G\) with respect to \(\beta\) is co-recursively enumerable (assuming that the set of generators of \(G\) is limit-recursive). In regard to the second question, it is proven that there is a generating sequence \(\beta\) for \(G\) such that every non-trivial finitely generated subgroup of \(G\) is recursively enumerable and the class of all such subgroups of \(G\) is behaviourally correctly learnable, that is, every non-trivial finitely generated subgroup can be semantically identified in the limit (again assuming that the set of generators of \(G\) is limit-recursive). On the other hand, the class of non-trivial finitely generated subgroups of \(G\) cannot be syntactically identified in the limit with respect to any generating sequence for \(G\). The present work thus contributes to a recent line of research studying algorithmically random infinite structures and uncovers an interesting connection between the arithmetical complexity of the set of generators of a randomly generated subgroup of rationals and the learnability of its finitely generated subgroups.}, address = {Dagstuhl, Germany}, annote = {Keywords: Martin-L{ö}f randomness, subgroups of rationals, finitely generated subgroups of rationals, learning in the limit, behaviourally correct learning}, author = {Gao, Ziyuan and Jain, Sanjay and Khoussainov, Bakhadyr and Li, Wei and Melnikov, Alexander and Seidel, Karen and Stephan, Frank}, booktitle = {International Symposium on Mathematical Foundations of Computer Science (MFCS)}, editor = {Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter}, keywords = {karenseidel mfcs year2019}, pages = {25:1-25:14}, publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, title = {Random Subgroups of Rationals}, volume = 138, year = 2019 }
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  Bilò, Davide; Friedrich, Tobias; Lenzner, Pascal; Melnichenko, Anna Geometric Network Creation Games. Symposium on Parallelism in Algorithms and Architectures (SPAA) 2019: 323-332
  [ Abstract ] [ BibTeX ] [ DOI ] [ Download ]
   
  Network Creation Games are a well-known approach for explaining and analyzing the structure, quality and dynamics of real-world networks like the Internet and other infrastructure networks which evolved via the interaction of selfish agents without a central authority. In these games selfish agents which correspond to nodes in a network strategically buy incident edges to improve their centrality. However, past research on these games has 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 depends 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.~[PODC'03] 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 non-constant bound on the Price of Anarchy for the metric version and a slightly weaker upper bound for the non-metric 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 a variant of the classical Network Design Problem. Thus, low-cost equilibria of our game correspond to decentralized and stable approximations of the optimum network design.
  @inproceedings{bil2019geometric, abstract = {Network Creation Games are a well-known approach for explaining and analyzing the structure, quality and dynamics of real-world networks like the Internet and other infrastructure networks which evolved via the interaction of selfish agents without a central authority. In these games selfish agents which correspond to nodes in a network strategically buy incident edges to improve their centrality. However, past research on these games has 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 depends 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.~[PODC'03] 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 non-constant bound on the Price of Anarchy for the metric version and a slightly weaker upper bound for the non-metric 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 a variant 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}, booktitle = {Symposium on Parallelism in Algorithms and Architectures (SPAA)}, keywords = {annamelnichenko davidebilo pascallenzner spaa tobiasfriedrich year2019}, pages = {323-332}, title = {Geometric Network Creation Games}, year = 2019 }
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  Friedrich, Tobias From Graph Theory to Network Science: The Natural Emergence of Hyperbolicity. Symposium Theoretical Aspects of Computer Science (STACS) 2019: 5:1–5:9
  [ Abstract ] [ BibTeX ] [ DOI ] [ Download ]
   
  Network science is driven by the question which properties large real-world networks have and how we can exploit them algorithmically. In the past few years, hyperbolic graphs have emerged as a very promising model for scale-free networks. The connection between hyperbolic geometry and complex networks gives insights in both directions: (1) Hyperbolic geometry forms the basis of a natural and explanatory model for real-world networks. Hyperbolic random graphs are obtained by choosing random points in the hyperbolic plane and connecting pairs of points that are geometrically close. The resulting networks share many structural properties for example with online social networks like Facebook or Twitter. They are thus well suited for algorithmic analyses in a more realistic setting. (2) Starting with a real-world network, hyperbolic geometry is well-suited for metric embeddings. The vertices of a network can be mapped to points in this geometry, such that geometric distances are similar to graph distances. Such embeddings have a variety of algorithmic applications ranging from approximations based on efficient geometric algorithms to greedy routing solely using hyperbolic coordinates for navigation decisions.
  @inproceedings{friedrich2019graph, abstract = {Network science is driven by the question which properties large real-world networks have and how we can exploit them algorithmically. In the past few years, hyperbolic graphs have emerged as a very promising model for scale-free networks. The connection between hyperbolic geometry and complex networks gives insights in both directions: (1) Hyperbolic geometry forms the basis of a natural and explanatory model for real-world networks. Hyperbolic random graphs are obtained by choosing random points in the hyperbolic plane and connecting pairs of points that are geometrically close. The resulting networks share many structural properties for example with online social networks like Facebook or Twitter. They are thus well suited for algorithmic analyses in a more realistic setting. (2) Starting with a real-world network, hyperbolic geometry is well-suited for metric embeddings. The vertices of a network can be mapped to points in this geometry, such that geometric distances are similar to graph distances. Such embeddings have a variety of algorithmic applications ranging from approximations based on efficient geometric algorithms to greedy routing solely using hyperbolic coordinates for navigation decisions.}, author = {Friedrich, Tobias}, booktitle = {Symposium Theoretical Aspects of Computer Science (STACS)}, keywords = {stacs tobiasfriedrich year2019}, pages = {5:1–5:9}, title = {From Graph Theory to Network Science: The Natural Emergence of Hyperbolicity}, year = 2019 }
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  Bläsius, Thomas; Friedrich, Tobias; Sutton, Andrew M. On the Empirical Time Complexity of Scale-Free 3-SAT at the Phase Transition. Tools and Algorithms for the Construction and Analysis of Systems (TACAS) 2019: 117-134
  [ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
   
  The hardness of formulas at the solubility phase transition of random propositional satisfiability (SAT) has been intensely studied for decades both empirically and theoretically. Solvers based on stochastic local search (SLS) appear to scale very well at the critical threshold, while complete backtracking solvers exhibit exponential scaling. On industrial SAT instances, this phenomenon is inverted: backtracking solvers can tackle large industrial problems, where SLS-based solvers appear to stall. Industrial instances exhibit sharply different structure than uniform random instances. Among many other properties, they are often heterogeneous in the sense that some variables appear in many while others appear in only few clauses. We conjecture that the heterogeneity of SAT formulas alone already contributes to the trade-off in performance between SLS solvers and complete backtracking solvers. We empirically determine how the run time of SLS vs. backtracking solvers depends on the heterogeneity of the input, which is controlled by drawing variables according to a scale-free distribution. Our experiments reveal that the efficiency of complete solvers at the phase transition is strongly related to the heterogeneity of the degree distribution. We report results that suggest the depth of satisfying assignments in complete search trees is influenced by the level of heterogeneity as measured by a power-law exponent. We also find that incomplete SLS solvers, which scale well on uniform instances, are not affected by heterogeneity. The main contribution of this paper utilizes the scale-free random 3-SAT model to isolate heterogeneity as an important factor in the scaling discrepancy between complete and SLS solvers at the uniform phase transition found in previous works.
  @inproceedings{blasius2019empirical, abstract = {The hardness of formulas at the solubility phase transition of random propositional satisfiability (SAT) has been intensely studied for decades both empirically and theoretically. Solvers based on stochastic local search (SLS) appear to scale very well at the critical threshold, while complete backtracking solvers exhibit exponential scaling. On industrial SAT instances, this phenomenon is inverted: backtracking solvers can tackle large industrial problems, where SLS-based solvers appear to stall. Industrial instances exhibit sharply different structure than uniform random instances. Among many other properties, they are often heterogeneous in the sense that some variables appear in many while others appear in only few clauses. We conjecture that the heterogeneity of SAT formulas alone already contributes to the trade-off in performance between SLS solvers and complete backtracking solvers. We empirically determine how the run time of SLS vs. backtracking solvers depends on the heterogeneity of the input, which is controlled by drawing variables according to a scale-free distribution. Our experiments reveal that the efficiency of complete solvers at the phase transition is strongly related to the heterogeneity of the degree distribution. We report results that suggest the depth of satisfying assignments in complete search trees is influenced by the level of heterogeneity as measured by a power-law exponent. We also find that incomplete SLS solvers, which scale well on uniform instances, are not affected by heterogeneity. The main contribution of this paper utilizes the scale-free random 3-SAT model to isolate heterogeneity as an important factor in the scaling discrepancy between complete and SLS solvers at the uniform phase transition found in previous works.}, author = {Bläsius, Thomas and Friedrich, Tobias and Sutton, Andrew M.}, booktitle = {Tools and Algorithms for the Construction and Analysis of Systems (TACAS)}, keywords = {andrewmsutton scalefree_sat tacas thomasblaesius tobiasfriedrich year2019}, pages = {117-134}, title = {On the Empirical Time Complexity of Scale-Free 3-SAT at the Phase Transition}, year = 2019 }
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  Bläsius, Thomas; Fischbeck, Philipp; Friedrich, Tobias; Schirneck, Martin Understanding the Effectiveness of Data Reduction in Public Transportation Networks. Workshop on Algorithms and Models for the Web Graph (WAW) 2019: 87-101
  [ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
   
  Given a public transportation network of stations and connections, we want to find a minimum subset of stations such that each connection runs through a selected station. Although this problem is NP-hard in general, real-world instances are regularly solved almost completely by a set of simple reduction rules. To explain this behavior, we view transportation networks as hitting set instances and identify two characteristic properties, locality and heterogeneity. We then devise a randomized model to generate hitting set instances with adjustable properties. While the heterogeneity does influence the effectiveness of the reduction rules, the generated instances show that locality is the significant factor. Beyond that, we prove that the effectiveness of the reduction rules is independent of the underlying graph structure. Finally, we show that high locality is also prevalent in instances from other domains, facilitating a fast computation of minimum hitting sets.
  @inproceedings{blasius2019understanding, abstract = {Given a public transportation network of stations and connections, we want to find a minimum subset of stations such that each connection runs through a selected station. Although this problem is NP-hard in general, real-world instances are regularly solved almost completely by a set of simple reduction rules. To explain this behavior, we view transportation networks as hitting set instances and identify two characteristic properties, locality and heterogeneity. We then devise a randomized model to generate hitting set instances with adjustable properties. While the heterogeneity does influence the effectiveness of the reduction rules, the generated instances show that locality is the significant factor. Beyond that, we prove that the effectiveness of the reduction rules is independent of the underlying graph structure. Finally, we show that high locality is also prevalent in instances from other domains, facilitating a fast computation of minimum hitting sets.}, author = {Bläsius, Thomas and Fischbeck, Philipp and Friedrich, Tobias and Schirneck, Martin}, booktitle = {Workshop on Algorithms and Models for the Web Graph (WAW)}, keywords = {martinschirneck philippfischbeck thomasblaesius tobiasfriedrich waw year2019}, pages = {87-101}, title = {Understanding the Effectiveness of Data Reduction in Public Transportation Networks}, year = 2019 }
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  Echzell, Hagen; Friedrich, Tobias; Lenzner, Pascal; Molitor, Louise; Pappik, Marcus; Schöne, Friedrich; Sommer, Fabian; Stangl, David Convergence and Hardness of Strategic Schelling Segregation. Web and Internet Economics (WINE) 2019: 156-170
  [ Abstract ] [ BibTeX ] [ DOI ] [ Download ]
   
  The phenomenon of residential segregation was captured by Schelling's famous segregation model where two types of agents are placed on a grid and an agent is content with her location if the fraction of her neighbors which have the same type as her is at least \(\tau\), for some \(0<\tau<1\). Discontent agents simply swap their location with a randomly chosen other discontent agent or jump to a random empty cell. We analyze a generalized game-theoretic model of Schelling segregation which allows more than two agent types and more general underlying graphs modeling the residential area. For this we show that both aspects heavily influence the dynamic properties and the tractability of finding an optimal placement. We map the boundary of when improving response dynamics (IRD), i.e., the natural approach for finding equilibrium states, are guaranteed to converge. For this we prove several sharp threshold results where guaranteed IRD convergence suddenly turns into the strongest possible non-convergence result: a violation of weak acyclicity. In particular, we show such threshold results also for Schelling's original model, which is in contrast to the standard assumption in many empirical papers. Furthermore, we show that in case of convergence, IRD find an equilibrium in \(O(m)\) steps, where \(m\) is the number of edges in the underlying graph and show that this bound is met in empirical simulations starting from random initial agent placements.
  @inproceedings{echzell2019convergence, abstract = {The phenomenon of residential segregation was captured by Schelling's famous segregation model where two types of agents are placed on a grid and an agent is content with her location if the fraction of her neighbors which have the same type as her is at least \(\tau\), for some \(0<\tau<1\). Discontent agents simply swap their location with a randomly chosen other discontent agent or jump to a random empty cell. We analyze a generalized game-theoretic model of Schelling segregation which allows more than two agent types and more general underlying graphs modeling the residential area. For this we show that both aspects heavily influence the dynamic properties and the tractability of finding an optimal placement. We map the boundary of when improving response dynamics (IRD), i.e., the natural approach for finding equilibrium states, are guaranteed to converge. For this we prove several sharp threshold results where guaranteed IRD convergence suddenly turns into the strongest possible non-convergence result: a violation of weak acyclicity. In particular, we show such threshold results also for Schelling's original model, which is in contrast to the standard assumption in many empirical papers. Furthermore, we show that in case of convergence, IRD find an equilibrium in \(O(m)\) steps, where \(m\) is the number of edges in the underlying graph and show that this bound is met in empirical simulations starting from random initial agent placements.}, author = {Echzell, Hagen and Friedrich, Tobias and Lenzner, Pascal and Molitor, Louise and Pappik, Marcus and Schöne, Friedrich and Sommer, Fabian and Stangl, David}, booktitle = {Web and Internet Economics (WINE)}, keywords = {louisemolitor pascallenzner tobiasfriedrich wine year2019}, pages = {156-170}, title = {Convergence and Hardness of Strategic Schelling Segregation}, year = 2019 }

2019

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  Friedrich, Tobias; Krejca, Martin S.; Rothenberger, Ralf; Arndt, Tobias; Hafner, Danijar; Kellermeier, Thomas; Krogmann, Simon; Razmjou, Armin Routing for On-Street Parking Search using Probabilistic Data. AI Communications 2019: 113-124
  [ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
   
  A significant percentage of urban traffic is caused by the search for parking spots. One possible approach to improve this situation is to guide drivers along routes which are likely to have free parking spots. The task of finding such a route can be modeled as a probabilistic graph problem which is NP-complete. Thus, we propose heuristic approaches for solving this problem and evaluate them experimentally. For this, we use probabilities of finding a parking spot, which are based on publicly available empirical data from TomTom International B.V. Additionally, we propose a heuristic that relies exclusively on conventional road attributes. Our experiments show that this algorithm comes close to the baseline by a factor of 1.3 in our cost measure. Last, we complement our experiments with results from a field study, comparing the success rates of our algorithms against real human drivers.
  @article{friedrich2019routing, abstract = {A significant percentage of urban traffic is caused by the search for parking spots. One possible approach to improve this situation is to guide drivers along routes which are likely to have free parking spots. The task of finding such a route can be modeled as a probabilistic graph problem which is NP-complete. Thus, we propose heuristic approaches for solving this problem and evaluate them experimentally. For this, we use probabilities of finding a parking spot, which are based on publicly available empirical data from TomTom International B.V. Additionally, we propose a heuristic that relies exclusively on conventional road attributes. Our experiments show that this algorithm comes close to the baseline by a factor of 1.3 in our cost measure. Last, we complement our experiments with results from a field study, comparing the success rates of our algorithms against real human drivers.}, author = {Friedrich, Tobias and Krejca, Martin S. and Rothenberger, Ralf and Arndt, Tobias and Hafner, Danijar and Kellermeier, Thomas and Krogmann, Simon and Razmjou, Armin}, journal = {AI Communications}, keywords = {arminrazmjou danijarhafner martinskrejca ralfrothenberger simonkrogmann thomaskellermeier tobiasarndt tobiasfriedrich year2019}, number = 2, pages = {113-124}, title = {Routing for On-Street Parking Search using Probabilistic Data}, volume = 32, year = 2019 }
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  Doerr, Benjamin; Doerr, Carola; Kötzing, Timo Solving Problems with Unknown Solution Length at Almost No Extra Cost. Algorithmica 2019: 703-748
  [ BibTeX ] [ URL ] [ DOI ] [ Download ]
   
  @article{DBLP:journals/algorithmica/DoerrDK19, author = {Doerr, Benjamin and Doerr, Carola and Kötzing, Timo}, journal = {Algorithmica}, keywords = {algorithmica benajmindoerr caroladoerr timokoetzing year2019}, number = 2, pages = {703-748}, title = {Solving Problems with Unknown Solution Length at Almost No Extra Cost}, volume = 81, year = 2019 }
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  Shi, Feng; Schirneck, Martin; Friedrich, Tobias; Kötzing, Timo; Neumann, Frank Reoptimization Time Analysis of Evolutionary Algorithms on Linear Functions Under Dynamic Uniform Constraints. Algorithmica 2019: 828-857
  [ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
   
  Rigorous runtime analysis is a major approach towards understanding evolutionary computing techniques, and in this area linear pseudo-Boolean objective functions play a central role. Having an additional linear constraint is then equivalent to the NP-hard Knapsack problem, certain classes thereof have been studied in recent works. In this article, we present a dynamic model of optimizing linear functions under uniform constraints. Starting from an optimal solution with respect to a given constraint bound, we investigate the runtimes that different evolutionary algorithms need to recompute an optimal solution when the constraint bound changes by a certain amount. The classical \((1+1)\) EA and several population-based algorithms are designed for that purpose, and are shown to recompute efficiently. Furthermore, a variant of the \((1+(\lambda,\lambda))\) GA for the dynamic optimization problem is studied, whose performance is better when the change of the constraint bound is small.
  @article{shi2019reoptimization, abstract = {Rigorous runtime analysis is a major approach towards understanding evolutionary computing techniques, and in this area linear pseudo-Boolean objective functions play a central role. Having an additional linear constraint is then equivalent to the NP-hard Knapsack problem, certain classes thereof have been studied in recent works. In this article, we present a dynamic model of optimizing linear functions under uniform constraints. Starting from an optimal solution with respect to a given constraint bound, we investigate the runtimes that different evolutionary algorithms need to recompute an optimal solution when the constraint bound changes by a certain amount. The classical \((1+1)\) EA and several population-based algorithms are designed for that purpose, and are shown to recompute efficiently. Furthermore, a variant of the \((1+(\lambda,\lambda))\) GA for the dynamic optimization problem is studied, whose performance is better when the change of the constraint bound is small.}, author = {Shi, Feng and Schirneck, Martin and Friedrich, Tobias and Kötzing, Timo and Neumann, Frank}, journal = {Algorithmica}, keywords = {algorithmica fengshi frankneumann martinschirneck timokoetzing tobiasfriedrich year2019}, number = 2, pages = {828-857}, title = {Reoptimization Time Analysis of Evolutionary Algorithms on Linear Functions Under Dynamic Uniform Constraints}, volume = 81, year = 2019 }
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  Doerr, Benjamin; Fischbeck, Philipp; Frahnow, Clemens; Friedrich, Tobias; Kötzing, Timo; Schirneck, Martin Island Models Meet Rumor Spreading. Algorithmica 2019: 886-915
  [ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
   
  Island models in evolutionary computation solve problems by a careful interplay of independently running evolutionary algorithms on the island and an exchange of good solutions between the islands. In this work, we conduct rigorous run time analyses for such island models trying to simultaneously obtain good run times and low communication effort. We improve the existing upper bounds for both measures (i) by improving the run time bounds via a careful analysis, (ii) by balancing individual computation and communication in a more appropriate manner, and (iii) by replacing the usual communicate-with-all approach with randomized rumor spreading. In the latter, each island contacts a randomly chosen neighbor. This epidemic communication paradigm is known to lead to very fast and robust information dissemination in many applications. Our results concern island models running simple (1+1) evolutionary algorithms to optimize the classic test functions OneMax and LeadingOnes. We investigate binary trees, d-dimensional tori, and complete graphs as communication topologies.
  @article{doerr2019island, abstract = {Island models in evolutionary computation solve problems by a careful interplay of independently running evolutionary algorithms on the island and an exchange of good solutions between the islands. In this work, we conduct rigorous run time analyses for such island models trying to simultaneously obtain good run times and low communication effort. We improve the existing upper bounds for both measures (i) by improving the run time bounds via a careful analysis, (ii) by balancing individual computation and communication in a more appropriate manner, and (iii) by replacing the usual communicate-with-all approach with randomized rumor spreading. In the latter, each island contacts a randomly chosen neighbor. This epidemic communication paradigm is known to lead to very fast and robust information dissemination in many applications. Our results concern island models running simple (1+1) evolutionary algorithms to optimize the classic test functions OneMax and LeadingOnes. We investigate binary trees, d-dimensional tori, and complete graphs as communication topologies.}, author = {Doerr, Benjamin and Fischbeck, Philipp and Frahnow, Clemens and Friedrich, Tobias and Kötzing, Timo and Schirneck, Martin}, journal = {Algorithmica}, keywords = {algorithmica benjamindoerr clemensfrahnow martinschirneck philippfischbeck timokoetzing tobiasfriedrich year2019}, month = {feb}, number = 2, pages = {886-915}, title = {Island Models Meet Rumor Spreading}, volume = 81, year = 2019 }
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  Gao, Ziyuan; Jain, Sanjay; Khoussainov, Bakhadyr; Li, Wei; Melnikov, Alexander; Seidel, Karen; Stephan, Frank Random Subgroups of Rationals. arXiv preprint arXiv:1901.04743 2019
  [ Abstract ] [ BibTeX ] [ Download ]
   
  This paper introduces and studies a notion of algorithmic randomness for subgroups of rationals. Given a randomly generated additive subgroup \((G,+)\) of rationals, two main questions are addressed: first, what are the model-theoretic and recursion-theoretic properties of \((G,+)\); second, what learnability properties can one extract from \(G\) and its subclass of finitely generated subgroups? For the first question, it is shown that the theory of \((G,+)\) coincides with that of the additive group of integers and is therefore decidable; furthermore, while the word problem for \(G\) with respect to any generating sequence for \(G\) is not even semi-decidable, one can build a generating sequence \(\beta\) such that the word problem for \(G\) with respect to \(\beta\) is co-recursively enumerable (assuming that the set of generators of \(G\) is limit-recursive). In regard to the second question, it is proven that there is a generating sequence \(\beta\) for \(G\) such that every non-trivial finitely generated subgroup of \(G\) is recursively enumerable and the class of all such subgroups of \(G\) is behaviourally correctly learnable, that is, every non-trivial finitely generated subgroup can be semantically identified in the limit (again assuming that the set of generators of \(G\) is limit-recursive). On the other hand, the class of non-trivial finitely generated subgroups of \(G\) cannot be syntactically identified in the limit with respect to any generating sequence for \(G\). The present work thus contributes to a recent line of research studying algorithmically random infinite structures and uncovers an interesting connection between the arithmetical complexity of the set of generators of a randomly generated subgroup of rationals and the learnability of its finitely generated subgroups.
  @article{gao2019random, abstract = {This paper introduces and studies a notion of algorithmic randomness for subgroups of rationals. Given a randomly generated additive subgroup \((G,+)\) of rationals, two main questions are addressed: first, what are the model-theoretic and recursion-theoretic properties of \((G,+)\); second, what learnability properties can one extract from \(G\) and its subclass of finitely generated subgroups? For the first question, it is shown that the theory of \((G,+)\) coincides with that of the additive group of integers and is therefore decidable; furthermore, while the word problem for \(G\) with respect to any generating sequence for \(G\) is not even semi-decidable, one can build a generating sequence \(\beta\) such that the word problem for \(G\) with respect to \(\beta\) is co-recursively enumerable (assuming that the set of generators of \(G\) is limit-recursive). In regard to the second question, it is proven that there is a generating sequence \(\beta\) for \(G\) such that every non-trivial finitely generated subgroup of \(G\) is recursively enumerable and the class of all such subgroups of \(G\) is behaviourally correctly learnable, that is, every non-trivial finitely generated subgroup can be semantically identified in the limit (again assuming that the set of generators of \(G\) is limit-recursive). On the other hand, the class of non-trivial finitely generated subgroups of \(G\) cannot be syntactically identified in the limit with respect to any generating sequence for \(G\). The present work thus contributes to a recent line of research studying algorithmically random infinite structures and uncovers an interesting connection between the arithmetical complexity of the set of generators of a randomly generated subgroup of rationals and the learnability of its finitely generated subgroups.}, author = {Gao, Ziyuan and Jain, Sanjay and Khoussainov, Bakhadyr and Li, Wei and Melnikov, Alexander and Seidel, Karen and Stephan, Frank}, journal = {arXiv preprint arXiv:1901.04743}, keywords = {karenseidel year2019}, title = {Random Subgroups of Rationals}, year = 2019 }
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  Battaglia, Francesco; Cucina, Domenico; Rizzo, Manuel Detection and estimation of additive outliers in seasonal time series. Computational Statistics 2019: 1-17
  [ Abstract ] [ BibTeX ] [ DOI ] [ Download ]
   
  The detection of outliers in a time series is an important issue because their presence may have serious negative effects on the analysis in many different ways. Moreover the presence of a complex seasonal pattern in the series could affect the properties of the usual outlier detection procedures. Therefore modelling the appropriate form of seasonality is a very important step when outliers are present in a seasonal time series. In this paper we present some procedures for detection and estimation of additive outliers when parametric seasonal models, in particular periodic autoregressive, are specified to fit the data. A simulation study is presented to evaluate the benefits and the drawbacks of the proposed procedure on a selection of seasonal time series. An application to three real time series is also examined.
  @article{noauthororeditor, abstract = {The detection of outliers in a time series is an important issue because their presence may have serious negative effects on the analysis in many different ways. Moreover the presence of a complex seasonal pattern in the series could affect the properties of the usual outlier detection procedures. Therefore modelling the appropriate form of seasonality is a very important step when outliers are present in a seasonal time series. In this paper we present some procedures for detection and estimation of additive outliers when parametric seasonal models, in particular periodic autoregressive, are specified to fit the data. A simulation study is presented to evaluate the benefits and the drawbacks of the proposed procedure on a selection of seasonal time series. An application to three real time series is also examined.}, author = {Battaglia, Francesco and Cucina, Domenico and Rizzo, Manuel}, journal = {Computational Statistics}, keywords = {domenicocucina francescobattaglia manuelrizzo myown year2019}, pages = {1-17}, title = {Detection and estimation of additive outliers in seasonal time series}, year = 2019 }
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  Issac, Davis; Chandran, L. Sunil; Zhou, Sanming Hadwiger's conjecture for squares of 2-trees. European Journal of Combinatorics 2019
  [ BibTeX ] [ Download ]
   
  @article{noauthororeditor, author = {Issac, Davis and Chandran, L. Sunil and Zhou, Sanming}, journal = {European Journal of Combinatorics}, keywords = {davisissac ejc lsunilchandran sanmingzhou year2019}, title = {Hadwiger's conjecture for squares of 2-trees}, volume = 76, year = 2019 }
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  Trubenova, Barbora; Kötzing, Timo; Krejca, Martin S.; Lehre, Per Kristian Surfing on the seascape: Adaptation in a changing environment. Evolution: International Journal of Organic Evolution 2019: 1356-1374
  [ Abstract ] [ BibTeX ] [ DOI ] [ Download ]
   
  The environment changes constantly at various time scales and, in order to survive, species need to keep adapting. Whether these species succeed in avoiding extinction is a major evolutionary question. Using a multilocus evolutionary model of a mutation‐limited population adapting under strong selection, we investigate the effects of the frequency of environmental fluctuations on adaptation. Our results rely on an “adaptive‐walk” approximation and use mathematical methods from evolutionary computation theory to investigate the interplay between fluctuation frequency, the similarity of environments, and the number of loci contributing to adaptation. First, we assume a linear additive fitness function, but later generalize our results to include several types of epistasis. We show that frequent environmental changes prevent populations from reaching a fitness peak, but they may also prevent the large fitness loss that occurs after a single environmental change. Thus, the population can survive, although not thrive, in a wide range of conditions. Furthermore, we show that in a frequently changing environment, the similarity of threats that a population faces affects the level of adaptation that it is able to achieve. We check and supplement our analytical results with simulations.
  @article{trubenova2019surfing, abstract = {The environment changes constantly at various time scales and, in order to survive, species need to keep adapting. Whether these species succeed in avoiding extinction is a major evolutionary question. Using a multilocus evolutionary model of a mutation‐limited population adapting under strong selection, we investigate the effects of the frequency of environmental fluctuations on adaptation. Our results rely on an “adaptive‐walk” approximation and use mathematical methods from evolutionary computation theory to investigate the interplay between fluctuation frequency, the similarity of environments, and the number of loci contributing to adaptation. First, we assume a linear additive fitness function, but later generalize our results to include several types of epistasis. We show that frequent environmental changes prevent populations from reaching a fitness peak, but they may also prevent the large fitness loss that occurs after a single environmental change. Thus, the population can survive, although not thrive, in a wide range of conditions. Furthermore, we show that in a frequently changing environment, the similarity of threats that a population faces affects the level of adaptation that it is able to achieve. We check and supplement our analytical results with simulations.}, author = {Trubenova, Barbora and Kötzing, Timo and Krejca, Martin S. and Lehre, Per Kristian}, journal = {Evolution: International Journal of Organic Evolution}, keywords = {sys:relevantfor:ae barboratrubenova ev martinskrejca perkristianlehre timokoetzing year2019}, number = 7, pages = {1356-1374}, title = {Surfing on the seascape: Adaptation in a changing environment}, volume = 73, year = 2019 }
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  Bläsius, Thomas; Rademacher, Marcel; Rutter, Ignaz How to Draw a Planarization. Graph Algorithms and Applications 2019: 653-682
  [ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
   
  We study the problem of computing straight-line drawings of non-planar graphs with few crossings. We assume that a crossing-minimization algorithm is applied first, yielding a planarization, i.e., a planar graph with a dummy vertex for each crossing, that fixes the topology of the resulting drawing. We present and evaluate two different approaches for drawing a planarization in such a way that the edges of the input graph are as straight as possible. The first approach is based on the planarity-preserving force-directed algorithm IMPRED [Simonetto et al. Computer Graphics Forum 2011], the second approach, which we call Geometric Planarization Drawing, iteratively moves vertices to their locally optimal positions in the given initial drawing. Our evaluation shows that both approaches significantly improve the initial drawing and that our geometric approach outperforms the force-directed approach. To the best of our knowledge, this is the first paper concerned with the generation of a straight-line drawing that respects an arbitrary planarization.
  @article{blasius2019planarization, abstract = {We study the problem of computing straight-line drawings of non-planar graphs with few crossings. We assume that a crossing-minimization algorithm is applied first, yielding a planarization, i.e., a planar graph with a dummy vertex for each crossing, that fixes the topology of the resulting drawing. We present and evaluate two different approaches for drawing a planarization in such a way that the edges of the input graph are as straight as possible. The first approach is based on the planarity-preserving force-directed algorithm IMPRED [Simonetto et al. Computer Graphics Forum 2011], the second approach, which we call Geometric Planarization Drawing, iteratively moves vertices to their locally optimal positions in the given initial drawing. Our evaluation shows that both approaches significantly improve the initial drawing and that our geometric approach outperforms the force-directed approach. To the best of our knowledge, this is the first paper concerned with the generation of a straight-line drawing that respects an arbitrary planarization.}, author = {Bläsius, Thomas and Rademacher, Marcel and Rutter, Ignaz}, journal = {Graph Algorithms and Applications}, keywords = {jgaa thomasblaesius year2019}, number = 4, pages = {653-682}, title = {How to Draw a Planarization}, volume = 23, year = 2019 }
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  Battaglia, Francesco; Cucina, Domenico; Rizzo, Manuel Parsimonious periodic autoregressive models for time series with evolving trend and seasonality. Statistics and Computing 2019: 1-15
  [ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
   
  This paper proposes an extension of Periodic AutoRegressive (PAR) modelling for time series with evolving features. The large scale of modern datasets, in fact, implies that the time span may subtend several evolving patterns of the underlying series, affecting also seasonality. The proposed model allows several regimes in time and a possibly different PAR process with a trend term in each regime. The means, autocorrelations and residual variances may change both with the regime and the season, resulting in a very large number of parameters. Therefore as a second step we propose a grouping procedure on the PAR parameters, in order to obtain a more parsimonious and concise model. The model selection procedure is a complex combinatorial problem, and it is solved basing on Genetic Algorithms that optimize an information criterion. The model is tested in both simulation studies and real data analysis from different fields, proving to be effective for a wide range of series with evolving features, and competitive with respect to more specific models.
  @article{battaglia2019parsimonious, abstract = {This paper proposes an extension of Periodic AutoRegressive (PAR) modelling for time series with evolving features. The large scale of modern datasets, in fact, implies that the time span may subtend several evolving patterns of the underlying series, affecting also seasonality. The proposed model allows several regimes in time and a possibly different PAR process with a trend term in each regime. The means, autocorrelations and residual variances may change both with the regime and the season, resulting in a very large number of parameters. Therefore as a second step we propose a grouping procedure on the PAR parameters, in order to obtain a more parsimonious and concise model. The model selection procedure is a complex combinatorial problem, and it is solved basing on Genetic Algorithms that optimize an information criterion. The model is tested in both simulation studies and real data analysis from different fields, proving to be effective for a wide range of series with evolving features, and competitive with respect to more specific models.}, author = {Battaglia, Francesco and Cucina, Domenico and Rizzo, Manuel}, journal = {Statistics and Computing}, keywords = {sys:relevantfor:ae domenicocucina francescobattaglia manuelrizzo sc year2019}, pages = {1-15}, title = {Parsimonious periodic autoregressive models for time series with evolving trend and seasonality}, year = 2019 }
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  Cucina, Domenico; Rizzo, Manuel; Ursu, Eugen Multiple changepoint detection for periodic autoregressive models with an application to river flow analysis. Stochastic Environmental Research and Risk Assessment 2019: 1137-1157
  [ BibTeX ] [ DOI ] [ Download ]
   
  @article{cucina2019multiple, author = {Cucina, Domenico and Rizzo, Manuel and Ursu, Eugen}, editor = {Springer}, journal = {Stochastic Environmental Research and Risk Assessment}, keywords = {domenicocucina eugenursu manuelrizzo myown serra year2019}, month = {jun}, number = 4, pages = {1137-1157}, title = {Multiple changepoint detection for periodic autoregressive models with an application to river flow analysis}, volume = 33, year = 2019 }
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  Friedrich, Tobias; Kötzing, Timo; Krejca, Martin S. Unbiasedness of Estimation-of-Distribution Algorithms. Theoretical Computer Science 2019: 46-59
  [ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
   
  In the context of black-box optimization, black-box complexity is used for understanding the inherent difficulty of a given optimization problem. Central to our understanding of nature-inspired search heuristics in this context is the notion of unbiasedness. Specialized black-box complexities have been developed in order to better understand the limitations of these heuristics – especially of (population-based) evolutionary algorithms (EAs). In contrast to this, we focus on a model for algorithms explicitly maintaining a probability distribution over the search space: so-called estimation-of-distribution algorithms (EDAs). We consider the recently introduced \(n\)-Bernoulli-\(\lambda\)-EDA framework, which subsumes, for example, the commonly known EDAs PBIL, UMDA, \(\lambda\)-MMAS\(_\textrm{IB}\), and cGA. We show that an \(n\)-Bernoulli-\(\lambda\)-EDA is unbiased if and only if its probability distribution satisfies a certain invariance property under isometric automorphisms of \([0, 1]^n\). By restricting how an \(n\)-Bernoulli-\(\lambda\)-EDA can perform an update, in a way common to many examples, we derive conciser characterizations, which are easy to verify. We demonstrate this by showing that our examples above are all unbiased.
  @article{friedrich2019unbiasedness, abstract = {In the context of black-box optimization, black-box complexity is used for understanding the inherent difficulty of a given optimization problem. Central to our understanding of nature-inspired search heuristics in this context is the notion of unbiasedness. Specialized black-box complexities have been developed in order to better understand the limitations of these heuristics – especially of (population-based) evolutionary algorithms (EAs). In contrast to this, we focus on a model for algorithms explicitly maintaining a probability distribution over the search space: so-called estimation-of-distribution algorithms (EDAs). We consider the recently introduced \(n\)-Bernoulli-\(\lambda\)-EDA framework, which subsumes, for example, the commonly known EDAs PBIL, UMDA, \(\lambda\)-MMAS\(_\textrm{IB}\), and cGA. We show that an \(n\)-Bernoulli-\(\lambda\)-EDA is unbiased if and only if its probability distribution satisfies a certain invariance property under isometric automorphisms of \([0, 1]^n\). By restricting how an \(n\)-Bernoulli-\(\lambda\)-EDA can perform an update, in a way common to many examples, we derive conciser characterizations, which are easy to verify. We demonstrate this by showing that our examples above are all unbiased.}, author = {Friedrich, Tobias and Kötzing, Timo and Krejca, Martin S.}, journal = {Theoretical Computer Science}, keywords = {martinskrejca tcs timokoetzing tobiasfriedrich year2019}, pages = {46-59}, title = {Unbiasedness of Estimation-of-Distribution Algorithms}, volume = 785, year = 2019 }
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  Kötzing, Timo; Krejca, Martin S. First-hitting times under drift. Theoretical Computer Science 2019: 51-69
  [ Abstract ] [ BibTeX ] [ DOI ] [ Download ]
   
  For the last ten years, almost every theoretical result concerning the expected run time of a randomized search heuristic used drift theory, making it the arguably most important tool in this domain. Its success is due to its ease of use and its powerful result: drift theory allows the user to derive bounds on the expected first-hitting time of a random process by bounding expected local changes of the process – the drift. This is usually far easier than bounding the expected first-hitting time directly. Due to the widespread use of drift theory, it is of utmost importance to have the best drift theorems possible. We improve the fundamental additive, multiplicative, and variable drift theorems by stating them in a form as general as possible and providing examples of why the restrictions we keep are still necessary. Our additive drift theorem for upper bounds only requires the process to be lower-bounded, that is, we remove unnecessary restrictions like a finite, discrete, or bounded state space. As corollaries, the same is true for our upper bounds in the case of variable and multiplicative drift. By bounding the step size of the process, we derive new lower-bounding multiplicative and variable drift theorems. Last, we also state theorems that are applicable when the process has a drift of 0, by using a drift on the variance of the process.
  @article{ktzing2019firsthitting, abstract = {For the last ten years, almost every theoretical result concerning the expected run time of a randomized search heuristic used drift theory, making it the arguably most important tool in this domain. Its success is due to its ease of use and its powerful result: drift theory allows the user to derive bounds on the expected first-hitting time of a random process by bounding expected local changes of the process – the drift. This is usually far easier than bounding the expected first-hitting time directly. Due to the widespread use of drift theory, it is of utmost importance to have the best drift theorems possible. We improve the fundamental additive, multiplicative, and variable drift theorems by stating them in a form as general as possible and providing examples of why the restrictions we keep are still necessary. Our additive drift theorem for upper bounds only requires the process to be lower-bounded, that is, we remove unnecessary restrictions like a finite, discrete, or bounded state space. As corollaries, the same is true for our upper bounds in the case of variable and multiplicative drift. By bounding the step size of the process, we derive new lower-bounding multiplicative and variable drift theorems. Last, we also state theorems that are applicable when the process has a drift of 0, by using a drift on the variance of the process.}, author = {Kötzing, Timo and Krejca, Martin S.}, journal = {Theoretical Computer Science}, keywords = {martinskrejca tcs timokoetzing year2019}, pages = {51-69}, title = {First-hitting times under drift}, volume = 796, year = 2019 }
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  Bilò, Davide; Lenzner, Pascal On the Tree Conjecture for the Network Creation Game. Theory of Computing Systems 2019: 1-22
  [ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
   
  Selfish Network Creation focuses on modeling real world networks from a game-theoretic point of view. One of the classic models by Fabrikant et al. (2003) is the network creation game, where agents correspond to nodes in a network which buy incident edges for the price of \($\alpha$\) per edge to minimize their total distance to all other nodes. The model is well-studied but still has intriguing open problems. The most famous conjectures state that the price of anarchy is constant for all \($\alpha$\) and that for \($\alpha \geq n$\) all equilibrium networks are trees. We introduce a novel technique for analyzing stable networks for high edge-price \($\alpha$\) and employ it to improve on the best known bound for the latter conjecture. In particular we show that for \($\alpha>4n −13$\) all equilibrium networks must be trees, which implies a constant price of anarchy for this range of \($\alpha$\). Moreover, we also improve the constant upper bound on the price of anarchy for equilibrium trees.
  @article{Bilò2019, abstract = {Selfish Network Creation focuses on modeling real world networks from a game-theoretic point of view. One of the classic models by Fabrikant et al. (2003) is the network creation game, where agents correspond to nodes in a network which buy incident edges for the price of $\alpha$ per edge to minimize their total distance to all other nodes. The model is well-studied but still has intriguing open problems. The most famous conjectures state that the price of anarchy is constant for all $\alpha$ and that for $\alpha \geq n$ all equilibrium networks are trees. We introduce a novel technique for analyzing stable networks for high edge-price $\alpha$ and employ it to improve on the best known bound for the latter conjecture. In particular we show that for $\alpha>4n −13$ all equilibrium networks must be trees, which implies a constant price of anarchy for this range of $\alpha$. Moreover, we also improve the constant upper bound on the price of anarchy for equilibrium trees.}, author = {Bil{ò}, Davide and Lenzner, Pascal}, journal = {Theory of Computing Systems}, keywords = {TOCS pascallenzner year2019}, month = {aug}, pages = {1-22}, title = {On the Tree Conjecture for the Network Creation Game}, year = 2019 }

2019

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  Friedrich, Tobias; Doerr, Carola; Arnold, Dirk V. Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms, FOGA 2019, Potsdam, Germany, August 27-29, 2019. 2019 ACM.

  Editorship
  [ BibTeX ] [ URL ] [ DOI ]
   
  @proceedings{DBLP:conf/foga/2019, author = {Friedrich, Tobias and Doerr, Carola and Arnold, Dirk V.}, keywords = {caroladoerr dirkarnold foga2019 tobiasfriedrich}, note = {Editorship}, publisher = {ACM}, title = {Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms, FOGA 2019, Potsdam, Germany, August 27-29, 2019}, year = 2019 }