18 Search Results for "Pongr�cz, Andr�s"

Document
DOI: 10.4230/LIPIcs.STACS.2024.34
Hardness of Linearly Ordered 4-Colouring of 3-Colourable 3-Uniform Hypergraphs

Authors: Marek Filakovský, Tamio-Vesa Nakajima, Jakub Opršal, Gianluca Tasinato, and Uli Wagner

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

Abstract
A linearly ordered (LO) k-colouring of a hypergraph is a colouring of its vertices with colours 1, … , k such that each edge contains a unique maximal colour. Deciding whether an input hypergraph admits LO k-colouring with a fixed number of colours is NP-complete (and in the special case of graphs, LO colouring coincides with the usual graph colouring). Here, we investigate the complexity of approximating the "linearly ordered chromatic number" of a hypergraph. We prove that the following promise problem is NP-complete: Given a 3-uniform hypergraph, distinguish between the case that it is LO 3-colourable, and the case that it is not even LO 4-colourable. We prove this result by a combination of algebraic, topological, and combinatorial methods, building on and extending a topological approach for studying approximate graph colouring introduced by Krokhin, Opršal, Wrochna, and Živný (2023).
Cite as

Marek Filakovský, Tamio-Vesa Nakajima, Jakub Opršal, Gianluca Tasinato, and Uli Wagner. Hardness of Linearly Ordered 4-Colouring of 3-Colourable 3-Uniform Hypergraphs. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 34:1-34:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{filakovsky_et_al:LIPIcs.STACS.2024.34,
  author =	{Filakovsk\'{y}, Marek and Nakajima, Tamio-Vesa and Opr\v{s}al, Jakub and Tasinato, Gianluca and Wagner, Uli},
  title =	{{Hardness of Linearly Ordered 4-Colouring of 3-Colourable 3-Uniform Hypergraphs}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{34:1--34:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.34},
  URN =		{urn:nbn:de:0030-drops-197445},
  doi =		{10.4230/LIPIcs.STACS.2024.34},
  annote =	{Keywords: constraint satisfaction problem, hypergraph colouring, promise problem, topological methods}
}
Document
DOI: 10.4230/LIPIcs.CP.2023.8
Symmetries for Cube-And-Conquer in Finite Model Finding

Authors: João Araújo, Choiwah Chow, and Mikoláš Janota

Published in: LIPIcs, Volume 280, 29th International Conference on Principles and Practice of Constraint Programming (CP 2023)

Abstract
The cube-and-conquer paradigm enables massive parallelization of SAT solvers, which has proven to be crucial in solving highly combinatorial problems. In this paper, we apply the paradigm in the context of finite model finding, where we show that isomorphic cubes can be discarded since they lead to isomorphic models. However, we are faced with the complication that a well-known technique, the Least Number Heuristic (LNH), already exists in finite model finders to effectively prune (some) isomorphic models from the search. Therefore, it needs to be shown that isomorphic cubes still can be discarded when the LNH is used. The presented ideas are incorporated into the finite model finder Mace4, where we demonstrate significant improvements in model enumeration.
Cite as

João Araújo, Choiwah Chow, and Mikoláš Janota. Symmetries for Cube-And-Conquer in Finite Model Finding. In 29th International Conference on Principles and Practice of Constraint Programming (CP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 280, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{araujo_et_al:LIPIcs.CP.2023.8,
  author =	{Ara\'{u}jo, Jo\~{a}o and Chow, Choiwah and Janota, Mikol\'{a}\v{s}},
  title =	{{Symmetries for Cube-And-Conquer in Finite Model Finding}},
  booktitle =	{29th International Conference on Principles and Practice of Constraint Programming (CP 2023)},
  pages =	{8:1--8:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-300-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{280},
  editor =	{Yap, Roland H. C.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2023.8},
  URN =		{urn:nbn:de:0030-drops-190455},
  doi =		{10.4230/LIPIcs.CP.2023.8},
  annote =	{Keywords: finite model enumeration, cube-and-conquer, symmetry-breaking, parallel algorithm, least number heuristic}
}
Document
DOI: 10.4230/LIPIcs.ITP.2023.19
MizAR 60 for Mizar 50

Authors: Jan Jakubův, Karel Chvalovský, Zarathustra Goertzel, Cezary Kaliszyk, Mirek Olšák, Bartosz Piotrowski, Stephan Schulz, Martin Suda, and Josef Urban

Published in: LIPIcs, Volume 268, 14th International Conference on Interactive Theorem Proving (ITP 2023)

Abstract
As a present to Mizar on its 50th anniversary, we develop an AI/TP system that automatically proves about 60% of the Mizar theorems in the hammer setting. We also automatically prove 75% of the Mizar theorems when the automated provers are helped by using only the premises used in the human-written Mizar proofs. We describe the methods and large-scale experiments leading to these results. This includes in particular the E and Vampire provers, their ENIGMA and Deepire learning modifications, a number of learning-based premise selection methods, and the incremental loop that interleaves growing a corpus of millions of ATP proofs with training increasingly strong AI/TP systems on them. We also present a selection of Mizar problems that were proved automatically.
Cite as

Jan Jakubův, Karel Chvalovský, Zarathustra Goertzel, Cezary Kaliszyk, Mirek Olšák, Bartosz Piotrowski, Stephan Schulz, Martin Suda, and Josef Urban. MizAR 60 for Mizar 50. In 14th International Conference on Interactive Theorem Proving (ITP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 268, pp. 19:1-19:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{jakubuv_et_al:LIPIcs.ITP.2023.19,
  author =	{Jakub\r{u}v, Jan and Chvalovsk\'{y}, Karel and Goertzel, Zarathustra and Kaliszyk, Cezary and Ol\v{s}\'{a}k, Mirek and Piotrowski, Bartosz and Schulz, Stephan and Suda, Martin and Urban, Josef},
  title =	{{MizAR 60 for Mizar 50}},
  booktitle =	{14th International Conference on Interactive Theorem Proving (ITP 2023)},
  pages =	{19:1--19:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-284-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{268},
  editor =	{Naumowicz, Adam and Thiemann, Ren\'{e}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2023.19},
  URN =		{urn:nbn:de:0030-drops-183942},
  doi =		{10.4230/LIPIcs.ITP.2023.19},
  annote =	{Keywords: Mizar, ENIGMA, Automated Reasoning, Machine Learning}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.22
On Polynomial Kernels for Traveling Salesperson Problem and Its Generalizations

Authors: Václav Blažej, Pratibha Choudhary, Dušan Knop, Šimon Schierreich, Ondřej Suchý, and Tomáš Valla

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
For many problems, the important instances from practice possess certain structure that one should reflect in the design of specific algorithms. As data reduction is an important and inextricable part of today’s computation, we employ one of the most successful models of such precomputation - the kernelization. Within this framework, we focus on Traveling Salesperson Problem (TSP) and some of its generalizations. We provide a kernel for TSP with size polynomial in either the feedback edge set number or the size of a modulator to constant-sized components. For its generalizations, we also consider other structural parameters such as the vertex cover number and the size of a modulator to constant-sized paths. We complement our results from the negative side by showing that the existence of a polynomial-sized kernel with respect to the fractioning number, the combined parameter maximum degree and treewidth, and, in the case of {Subset TSP}, modulator to disjoint cycles (i.e., the treewidth two graphs) is unlikely.
Cite as

Václav Blažej, Pratibha Choudhary, Dušan Knop, Šimon Schierreich, Ondřej Suchý, and Tomáš Valla. On Polynomial Kernels for Traveling Salesperson Problem and Its Generalizations. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 22:1-22:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{blazej_et_al:LIPIcs.ESA.2022.22,
  author =	{Bla\v{z}ej, V\'{a}clav and Choudhary, Pratibha and Knop, Du\v{s}an and Schierreich, \v{S}imon and Such\'{y}, Ond\v{r}ej and Valla, Tom\'{a}\v{s}},
  title =	{{On Polynomial Kernels for Traveling Salesperson Problem and Its Generalizations}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{22:1--22:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.22},
  URN =		{urn:nbn:de:0030-drops-169600},
  doi =		{10.4230/LIPIcs.ESA.2022.22},
  annote =	{Keywords: Traveling Salesperson, Subset TSP, Waypoint Routing, Kernelization}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.73
Scheduling Kernels via Configuration LP

Authors: Dušan Knop and Martin Koutecký

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
Makespan minimization (on parallel identical or unrelated machines) is arguably the most natural and studied scheduling problem. A common approach in practical algorithm design is to reduce the size of a given instance by a fast preprocessing step while being able to recover key information even after this reduction. This notion is formally studied as kernelization (or simply, kernel) - a polynomial time procedure which yields an equivalent instance whose size is bounded in terms of some given parameter. It follows from known results that makespan minimization parameterized by the longest job processing time p_max has a kernelization yielding a reduced instance whose size is exponential in p_max. Can this be reduced to polynomial in p_max? We answer this affirmatively not only for makespan minimization, but also for the (more complicated) objective of minimizing the weighted sum of completion times, also in the setting of unrelated machines when the number of machine kinds is a parameter. Our algorithm first solves the Configuration LP and based on its solution constructs a solution of an intermediate problem, called huge N-fold integer programming. This solution is further reduced in size by a series of steps, until its encoding length is polynomial in the parameters. Then, we show that huge N-fold IP is in NP, which implies that there is a polynomial reduction back to our scheduling problem, yielding a kernel. Our technique is highly novel in the context of kernelization, and our structural theorem about the Configuration LP is of independent interest. Moreover, we show a polynomial kernel for huge N-fold IP conditional on whether the so-called separation subproblem can be solved in polynomial time. Considering that integer programming does not admit polynomial kernels except for quite restricted cases, our "conditional kernel" provides new insight.
Cite as

Dušan Knop and Martin Koutecký. Scheduling Kernels via Configuration LP. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 73:1-73:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{knop_et_al:LIPIcs.ESA.2022.73,
  author =	{Knop, Du\v{s}an and Kouteck\'{y}, Martin},
  title =	{{Scheduling Kernels via Configuration LP}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{73:1--73:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.73},
  URN =		{urn:nbn:de:0030-drops-170118},
  doi =		{10.4230/LIPIcs.ESA.2022.73},
  annote =	{Keywords: Scheduling, Kernelization}
}
Document
DOI: 10.4230/LIPIcs.ITP.2022.16
The Isabelle ENIGMA

Authors: Zarathustra A. Goertzel, Jan Jakubův, Cezary Kaliszyk, Miroslav Olšák, Jelle Piepenbrock, and Josef Urban

Published in: LIPIcs, Volume 237, 13th International Conference on Interactive Theorem Proving (ITP 2022)

Abstract
We significantly improve the performance of the E automated theorem prover on the Isabelle Sledgehammer problems by combining learning and theorem proving in several ways. In particular, we develop targeted versions of the ENIGMA guidance for the Isabelle problems, targeted versions of neural premise selection, and targeted strategies for E. The methods are trained in several iterations over hundreds of thousands untyped and typed first-order problems extracted from Isabelle. Our final best single-strategy ENIGMA and premise selection system improves the best previous version of E by 25.3% in 15 seconds, outperforming also all other previous ATP and SMT systems.
Cite as

Zarathustra A. Goertzel, Jan Jakubův, Cezary Kaliszyk, Miroslav Olšák, Jelle Piepenbrock, and Josef Urban. The Isabelle ENIGMA. In 13th International Conference on Interactive Theorem Proving (ITP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 237, pp. 16:1-16:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{goertzel_et_al:LIPIcs.ITP.2022.16,
  author =	{Goertzel, Zarathustra A. and Jakub\r{u}v, Jan and Kaliszyk, Cezary and Ol\v{s}\'{a}k, Miroslav and Piepenbrock, Jelle and Urban, Josef},
  title =	{{The Isabelle ENIGMA}},
  booktitle =	{13th International Conference on Interactive Theorem Proving (ITP 2022)},
  pages =	{16:1--16:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-252-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{237},
  editor =	{Andronick, June and de Moura, Leonardo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2022.16},
  URN =		{urn:nbn:de:0030-drops-167253},
  doi =		{10.4230/LIPIcs.ITP.2022.16},
  annote =	{Keywords: E Prover, ENIGMA, Premise Selection, Isabelle/Sledgehammer}
}
Document
DOI: 10.4230/LIPIcs.SAT.2022.7
Towards Learning Quantifier Instantiation in SMT

Authors: Mikoláš Janota, Jelle Piepenbrock, and Bartosz Piotrowski

Published in: LIPIcs, Volume 236, 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)

Abstract
This paper applies machine learning (ML) to solve quantified satisfiability modulo theories (SMT) problems more efficiently. The motivating idea is that the solver should learn from already solved formulas to solve new ones. This is especially relevant in classes of similar formulas. We focus on the enumerative instantiation - a well-established approach to solving quantified formulas anchored in the Herbrand’s theorem. The task is to select the right ground terms to be instantiated. In ML parlance, this means learning to rank ground terms. We devise a series of features of the considered terms and train on them using boosted decision trees. In particular, we integrate the LightGBM library into the SMT solver cvc5. The experimental results demonstrate that the ML-guided solver enables us to solve more formulas than the base solver and reduce the number of quantifier instantiations. We also do an ablation study on the features used in the machine learning component, showing the contributions of the various additions.
Cite as

Mikoláš Janota, Jelle Piepenbrock, and Bartosz Piotrowski. Towards Learning Quantifier Instantiation in SMT. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{janota_et_al:LIPIcs.SAT.2022.7,
  author =	{Janota, Mikol\'{a}\v{s} and Piepenbrock, Jelle and Piotrowski, Bartosz},
  title =	{{Towards Learning Quantifier Instantiation in SMT}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-242-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{236},
  editor =	{Meel, Kuldeep S. and Strichman, Ofer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2022.7},
  URN =		{urn:nbn:de:0030-drops-166810},
  doi =		{10.4230/LIPIcs.SAT.2022.7},
  annote =	{Keywords: satisfiability modulo theories, quantifier instantiation, machine learning}
}
Document
DOI: 10.4230/LIPIcs.SAT.2022.29
SAT-Based Leximax Optimisation Algorithms

Authors: Miguel Cabral, Mikoláš Janota, and Vasco Manquinho

Published in: LIPIcs, Volume 236, 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)

Abstract
In several real-world problems, it is often the case that the goal is to optimise several objective functions. However, usually there is not a single optimal objective vector. Instead, there are many optimal objective vectors known as Pareto-optima. Finding all Pareto-optima is computationally expensive and the number of Pareto-optima can be too large for a user to analyse. A compromise can be made by defining an optimisation criterion that integrates all objective functions. In this paper we propose several SAT-based algorithms to solve multi-objective optimisation problems using the leximax criterion. The leximax criterion is used to obtain a Pareto-optimal solution with a small trade-off between the objective functions, which is suitable in problems where there is an absence of priorities between the objective functions. Experimental results on the Multi-Objective Package Upgradeability Optimisation problem show that the SAT-based algorithms are able to outperform the Integer Linear Programming (ILP) approach when using non-commercial ILP solvers. Additionally, experimental results on selected instances from the MaxSAT evaluation adapted to the multi-objective domain show that our approach outperforms the ILP approach using commercial solvers.
Cite as

Miguel Cabral, Mikoláš Janota, and Vasco Manquinho. SAT-Based Leximax Optimisation Algorithms. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 29:1-29:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{cabral_et_al:LIPIcs.SAT.2022.29,
  author =	{Cabral, Miguel and Janota, Mikol\'{a}\v{s} and Manquinho, Vasco},
  title =	{{SAT-Based Leximax Optimisation Algorithms}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{29:1--29:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-242-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{236},
  editor =	{Meel, Kuldeep S. and Strichman, Ofer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2022.29},
  URN =		{urn:nbn:de:0030-drops-167030},
  doi =		{10.4230/LIPIcs.SAT.2022.29},
  annote =	{Keywords: Multi-Objective Optimisation, Leximax, Sorting Networks}
}
Document
Short Paper
DOI: 10.4230/LIPIcs.CP.2021.4
Filtering Isomorphic Models by Invariants (Short Paper)

Authors: João Araújo, Choiwah Chow, and Mikoláš Janota

Published in: LIPIcs, Volume 210, 27th International Conference on Principles and Practice of Constraint Programming (CP 2021)

Abstract
The enumeration of finite models of first order logic formulas is an indispensable tool in computational algebra. The task is hindered by the existence of isomorphic models, which are of no use to mathematicians and therefore are typically filtered out a posteriori. This paper proposes a divide-and-conquer approach to speed up and parallelize this process. We design a series of invariant properties that enable us to partition existing models into mutually non-isomorphic blocks, which are then tackled separately. The presented approach is integrated into the popular tool Mace4, where it shows tremendous speed-ups for a variety of algebraic structures.
Cite as

João Araújo, Choiwah Chow, and Mikoláš Janota. Filtering Isomorphic Models by Invariants (Short Paper). In 27th International Conference on Principles and Practice of Constraint Programming (CP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 210, pp. 4:1-4:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{araujo_et_al:LIPIcs.CP.2021.4,
  author =	{Ara\'{u}jo, Jo\~{a}o and Chow, Choiwah and Janota, Mikol\'{a}\v{s}},
  title =	{{Filtering Isomorphic Models by Invariants}},
  booktitle =	{27th International Conference on Principles and Practice of Constraint Programming (CP 2021)},
  pages =	{4:1--4:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-211-2},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{210},
  editor =	{Michel, Laurent D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2021.4},
  URN =		{urn:nbn:de:0030-drops-152956},
  doi =		{10.4230/LIPIcs.CP.2021.4},
  annote =	{Keywords: finite model enumeration, isomorphism, invariants, Mace4}
}
Document
DOI: 10.4230/LIPIcs.CP.2021.23
Bounds on Weighted CSPs Using Constraint Propagation and Super-Reparametrizations

Authors: Tomáš Dlask, Tomáš Werner, and Simon de Givry

Published in: LIPIcs, Volume 210, 27th International Conference on Principles and Practice of Constraint Programming (CP 2021)

Abstract
We propose a framework for computing upper bounds on the optimal value of the (maximization version of) Weighted CSP (WCSP) using super-reparametrizations, which are changes of the weights that keep or increase the WCSP objective for every assignment. We show that it is in principle possible to employ arbitrary (under certain technical conditions) constraint propagation rules to improve the bound. For arc consistency in particular, the method reduces to the known Virtual AC (VAC) algorithm. Newly, we implemented the method for singleton arc consistency (SAC) and compared it to other strong local consistencies in WCSPs on a public benchmark. The results show that the bounds obtained from SAC are superior for many instance groups.
Cite as

Tomáš Dlask, Tomáš Werner, and Simon de Givry. Bounds on Weighted CSPs Using Constraint Propagation and Super-Reparametrizations. In 27th International Conference on Principles and Practice of Constraint Programming (CP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 210, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{dlask_et_al:LIPIcs.CP.2021.23,
  author =	{Dlask, Tom\'{a}\v{s} and Werner, Tom\'{a}\v{s} and de Givry, Simon},
  title =	{{Bounds on Weighted CSPs Using Constraint Propagation and Super-Reparametrizations}},
  booktitle =	{27th International Conference on Principles and Practice of Constraint Programming (CP 2021)},
  pages =	{23:1--23:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-211-2},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{210},
  editor =	{Michel, Laurent D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2021.23},
  URN =		{urn:nbn:de:0030-drops-153149},
  doi =		{10.4230/LIPIcs.CP.2021.23},
  annote =	{Keywords: Weighted CSP, Super-Reparametrization, Linear Programming, Constraint Propagation}
}
Document
DOI: 10.4230/LIPIcs.CP.2021.31
The Seesaw Algorithm: Function Optimization Using Implicit Hitting Sets

Authors: Mikoláš Janota, António Morgado, José Fragoso Santos, and Vasco Manquinho

Published in: LIPIcs, Volume 210, 27th International Conference on Principles and Practice of Constraint Programming (CP 2021)

Abstract
The paper introduces the Seesaw algorithm, which explores the Pareto frontier of two given functions. The algorithm is complete and generalizes the well-known implicit hitting set paradigm. The first given function determines a cost of a hitting set and is optimized by an exact solver. The second, called the oracle function, is treated as a black-box. This approach is particularly useful in the optimization of functions that are impossible to encode into an exact solver. We show the effectiveness of the algorithm in the context of static solver portfolio selection. The existing implicit hitting set paradigm is applied to cost function and an oracle predicate. Hence, the Seesaw algorithm generalizes this by enabling the oracle to be a function. The paper identifies two independent preconditions that guarantee the correctness of the algorithm. This opens a number of avenues for future research into the possible instantiations of the algorithm, depending on the cost and oracle functions used.
Cite as

Mikoláš Janota, António Morgado, José Fragoso Santos, and Vasco Manquinho. The Seesaw Algorithm: Function Optimization Using Implicit Hitting Sets. In 27th International Conference on Principles and Practice of Constraint Programming (CP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 210, pp. 31:1-31:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{janota_et_al:LIPIcs.CP.2021.31,
  author =	{Janota, Mikol\'{a}\v{s} and Morgado, Ant\'{o}nio and Fragoso Santos, Jos\'{e} and Manquinho, Vasco},
  title =	{{The Seesaw Algorithm: Function Optimization Using Implicit Hitting Sets}},
  booktitle =	{27th International Conference on Principles and Practice of Constraint Programming (CP 2021)},
  pages =	{31:1--31:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-211-2},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{210},
  editor =	{Michel, Laurent D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2021.31},
  URN =		{urn:nbn:de:0030-drops-153220},
  doi =		{10.4230/LIPIcs.CP.2021.31},
  annote =	{Keywords: implicit hitting sets, minimal hitting set, MaxSAT, optimization}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2020.8
Recognizing Proper Tree-Graphs

Authors: Steven Chaplick, Petr A. Golovach, Tim A. Hartmann, and Dušan Knop

Published in: LIPIcs, Volume 180, 15th International Symposium on Parameterized and Exact Computation (IPEC 2020)

Abstract
We investigate the parameterized complexity of the recognition problem for the proper H-graphs. The H-graphs are the intersection graphs of connected subgraphs of a subdivision of a multigraph H, and the properness means that the containment relationship between the representations of the vertices is forbidden. The class of H-graphs was introduced as a natural (parameterized) generalization of interval and circular-arc graphs by Biró, Hujter, and Tuza in 1992, and the proper H-graphs were introduced by Chaplick et al. in WADS 2019 as a generalization of proper interval and circular-arc graphs. For these graph classes, H may be seen as a structural parameter reflecting the distance of a graph to a (proper) interval graph, and as such gained attention as a structural parameter in the design of efficient algorithms. We show the following results. - For a tree T with t nodes, it can be decided in 2^{𝒪(t² log t)} ⋅ n³ time, whether an n-vertex graph G is a proper T-graph. For yes-instances, our algorithm outputs a proper T-representation. This proves that the recognition problem for proper H-graphs, where H required to be a tree, is fixed-parameter tractable when parameterized by the size of T. Previously only NP-completeness was known. - Contrasting to the first result, we prove that if H is not constrained to be a tree, then the recognition problem becomes much harder. Namely, we show that there is a multigraph H with 4 vertices and 5 edges such that it is NP-complete to decide whether G is a proper H-graph.
Cite as

Steven Chaplick, Petr A. Golovach, Tim A. Hartmann, and Dušan Knop. Recognizing Proper Tree-Graphs. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 8:1-8:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{chaplick_et_al:LIPIcs.IPEC.2020.8,
  author =	{Chaplick, Steven and Golovach, Petr A. and Hartmann, Tim A. and Knop, Du\v{s}an},
  title =	{{Recognizing Proper Tree-Graphs}},
  booktitle =	{15th International Symposium on Parameterized and Exact Computation (IPEC 2020)},
  pages =	{8:1--8:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-172-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{180},
  editor =	{Cao, Yixin and Pilipczuk, Marcin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2020.8},
  URN =		{urn:nbn:de:0030-drops-133118},
  doi =		{10.4230/LIPIcs.IPEC.2020.8},
  annote =	{Keywords: intersection graphs, H-graphs, recognition, fixed-parameter tractability}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2020.16
Approximation Algorithms for Steiner Tree Based on Star Contractions: A Unified View

Authors: Radek Hušek, Dušan Knop, and Tomáš Masařk

Published in: LIPIcs, Volume 180, 15th International Symposium on Parameterized and Exact Computation (IPEC 2020)

Abstract
In the Steiner Tree problem, we are given an edge-weighted undirected graph G = (V,E) and a set of terminals R ⊆ V. The task is to find a connected subgraph of G containing R and minimizing the sum of weights of its edges. Steiner Tree is well known to be NP-complete and is undoubtedly one of the most studied problems in (applied) computer science. We observe that many approximation algorithms for Steiner Tree follow a similar scheme (meta-algorithm) and perform (exhaustively) a similar routine which we call star contraction. Here, by a star contraction, we mean finding a star-like subgraph in (the metric closure of) the input graph minimizing the ratio of its weight to the number of contained terminals minus one; and contract. It is not hard to see that the well-known MST-approximation seeks the best star to contract among those containing two terminals only. Zelikovsky’s approximation algorithm follows a similar workflow, finding the best star among those containing three terminals. We perform an empirical study of star contractions with the relaxed condition on the number of terminals in each star contraction motivated by a recent result of Dvořák et al. [Parameterized Approximation Schemes for Steiner Trees with Small Number of Steiner Vertices, STACS 2018]. Furthermore, we propose two improvements of Zelikovsky’s 11/6-approximation algorithm and we empirically confirm that the quality of the solution returned by any of these is better than the one returned by the former algorithm. However, such an improvement is exchanged for a slower running time (up to a multiplicative factor of the number of terminals).
Cite as

Radek Hušek, Dušan Knop, and Tomáš Masařk. Approximation Algorithms for Steiner Tree Based on Star Contractions: A Unified View. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{husek_et_al:LIPIcs.IPEC.2020.16,
  author =	{Hu\v{s}ek, Radek and Knop, Du\v{s}an and Masa\v{r}k, Tom\'{a}\v{s}},
  title =	{{Approximation Algorithms for Steiner Tree Based on Star Contractions: A Unified View}},
  booktitle =	{15th International Symposium on Parameterized and Exact Computation (IPEC 2020)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-172-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{180},
  editor =	{Cao, Yixin and Pilipczuk, Marcin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2020.16},
  URN =		{urn:nbn:de:0030-drops-133193},
  doi =		{10.4230/LIPIcs.IPEC.2020.16},
  annote =	{Keywords: Steiner tree, approximation, star contractions, minimum spanning tree}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2020.36
Length-Bounded Cuts: Proper Interval Graphs and Structural Parameters

Authors: Matthias Bentert, Klaus Heeger, and Dušan Knop

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract
In the presented paper, we study the Length-Bounded Cut problem for special graph classes as well as from a parameterized-complexity viewpoint. Here, we are given a graph G, two vertices s and t, and positive integers β and λ. The task is to find a set F of edges of size at most β such that every s-t-path of length at most λ in G contains some edge in F. Bazgan et al. [Networks, 2019] conjectured that Length-Bounded Cut admits a polynomial-time algorithm if the input graph G is a proper interval graph. We confirm this conjecture by providing a dynamic-programming based polynomial-time algorithm. Moreover, we strengthen the W[1]-hardness result of Dvořák and Knop [Algorithmica, 2018] for Length-Bounded Cut parameterized by pathwidth. Our reduction is shorter, and the target of the reduction has stronger structural properties. Consequently, we give W[1]-hardness for the combined parameter pathwidth and maximum degree of the input graph. Finally, we prove that Length-Bounded Cut is W[1]-hard for the feedback vertex number. Both our hardness results complement known XP algorithms.
Cite as

Matthias Bentert, Klaus Heeger, and Dušan Knop. Length-Bounded Cuts: Proper Interval Graphs and Structural Parameters. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 36:1-36:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bentert_et_al:LIPIcs.ISAAC.2020.36,
  author =	{Bentert, Matthias and Heeger, Klaus and Knop, Du\v{s}an},
  title =	{{Length-Bounded Cuts: Proper Interval Graphs and Structural Parameters}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{36:1--36:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.36},
  URN =		{urn:nbn:de:0030-drops-133800},
  doi =		{10.4230/LIPIcs.ISAAC.2020.36},
  annote =	{Keywords: Edge-disjoint paths, pathwidth, feedback vertex number}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2020.61
Bounding Radon Number via Betti Numbers

Authors: Zuzana Patáková

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract
We prove general topological Radon-type theorems for sets in ℝ^d, smooth real manifolds or finite dimensional simplicial complexes. Combined with a recent result of Holmsen and Lee, it gives fractional Helly theorem, and consequently the existence of weak ε-nets as well as a (p,q)-theorem. More precisely: Let X be either ℝ^d, smooth real d-manifold, or a finite d-dimensional simplicial complex. Then if F is a finite, intersection-closed family of sets in X such that the ith reduced Betti number (with ℤ₂ coefficients) of any set in F is at most b for every non-negative integer i less or equal to k, then the Radon number of F is bounded in terms of b and X. Here k is the smallest integer larger or equal to d/2 - 1 if X = ℝ^d; k=d-1 if X is a smooth real d-manifold and not a surface, k=0 if X is a surface and k=d if X is a d-dimensional simplicial complex. Using the recent result of the author and Kalai, we manage to prove the following optimal bound on fractional Helly number for families of open sets in a surface: Let F be a finite family of open sets in a surface S such that the intersection of any subfamily of F is either empty, or path-connected. Then the fractional Helly number of F is at most three. This also settles a conjecture of Holmsen, Kim, and Lee about an existence of a (p,q)-theorem for open subsets of a surface.
Cite as

Zuzana Patáková. Bounding Radon Number via Betti Numbers. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 61:1-61:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{patakova:LIPIcs.SoCG.2020.61,
  author =	{Pat\'{a}kov\'{a}, Zuzana},
  title =	{{Bounding Radon Number via Betti Numbers}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{61:1--61:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.61},
  URN =		{urn:nbn:de:0030-drops-122198},
  doi =		{10.4230/LIPIcs.SoCG.2020.61},
  annote =	{Keywords: Radon number, topological complexity, constrained chain maps, fractional Helly theorem, convexity spaces}
}
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