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Documents authored by Kirchweger, Markus

Document
Short Paper
DOI: 10.4230/LIPIcs.CP.2024.37
Computing Small Rainbow Cycle Numbers with SAT Modulo Symmetries (Short Paper)

Authors: Markus Kirchweger and Stefan Szeider

Published in: LIPIcs, Volume 307, 30th International Conference on Principles and Practice of Constraint Programming (CP 2024)

Abstract
Envy-freeness up to any good (EFX) is a key concept in Computational Social Choice for the fair division of indivisible goods, where no agent envies another’s allocation after removing any single item. A deeper understanding of EFX allocations is facilitated by exploring the rainbow cycle number (R_f(d)), the largest number of independent sets in a certain class of directed graphs. Upper bounds on R_f(d) provide guarantees to the feasibility of EFX allocations (Chaudhury et al., EC 2021). In this work, we precisely compute the numbers R_f(d) for small values of d, employing the SAT modulo Symmetries framework (Kirchweger and Szeider, CP 2021). SAT modulo Symmetries is tailored specifically for the constraint-based isomorph-free generation of combinatorial structures. We provide an efficient encoding for the rainbow cycle number, comparing eager and lazy approaches. To cope with the huge search space, we extend the encoding with invariant pruning, a new method that significantly speeds up computation.
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Markus Kirchweger and Stefan Szeider. Computing Small Rainbow Cycle Numbers with SAT Modulo Symmetries (Short Paper). In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 37:1-37:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kirchweger_et_al:LIPIcs.CP.2024.37,
  author =	{Kirchweger, Markus and Szeider, Stefan},
  title =	{{Computing Small Rainbow Cycle Numbers with SAT Modulo Symmetries}},
  booktitle =	{30th International Conference on Principles and Practice of Constraint Programming (CP 2024)},
  pages =	{37:1--37:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-336-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{307},
  editor =	{Shaw, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2024.37},
  URN =		{urn:nbn:de:0030-drops-207221},
  doi =		{10.4230/LIPIcs.CP.2024.37},
  annote =	{Keywords: EFX, rainbow cycle number, SAT modulo Symmetries, combinatorial search}
}
Document
DOI: 10.4230/LIPIcs.SAT.2023.8
IPASIR-UP: User Propagators for CDCL

Authors: Katalin Fazekas, Aina Niemetz, Mathias Preiner, Markus Kirchweger, Stefan Szeider, and Armin Biere

Published in: LIPIcs, Volume 271, 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)

Abstract
Modern SAT solvers are frequently embedded as sub-reasoning engines into more complex tools for addressing problems beyond the Boolean satisfiability problem. Examples include solvers for Satisfiability Modulo Theories (SMT), combinatorial optimization, model enumeration and counting. In such use cases, the SAT solver is often able to provide relevant information beyond the satisfiability answer. Further, domain knowledge of the embedding system (e.g., symmetry properties or theory axioms) can be beneficial for the CDCL search, but cannot be efficiently represented in clausal form. In this paper, we propose a general interface to inspect and influence the internal behaviour of CDCL SAT solvers. Our goal is to capture the most essential functionalities that are sufficient to simplify and improve use cases that require a more fine-grained interaction with the SAT solver than provided via the standard IPASIR interface. For our experiments, we extend CaDiCaL with our interface and evaluate it on two representative use cases: enumerating graphs within the SAT modulo Symmetries framework (SMS), and as the main CDCL(T) SAT engine of the SMT solver cvc5.
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Katalin Fazekas, Aina Niemetz, Mathias Preiner, Markus Kirchweger, Stefan Szeider, and Armin Biere. IPASIR-UP: User Propagators for CDCL. In 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 271, pp. 8:1-8:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{fazekas_et_al:LIPIcs.SAT.2023.8,
  author =	{Fazekas, Katalin and Niemetz, Aina and Preiner, Mathias and Kirchweger, Markus and Szeider, Stefan and Biere, Armin},
  title =	{{IPASIR-UP: User Propagators for CDCL}},
  booktitle =	{26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)},
  pages =	{8:1--8:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-286-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{271},
  editor =	{Mahajan, Meena and Slivovsky, Friedrich},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2023.8},
  URN =		{urn:nbn:de:0030-drops-184709},
  doi =		{10.4230/LIPIcs.SAT.2023.8},
  annote =	{Keywords: SAT, CDCL, Satisfiability Modulo Theories, Satisfiability Modulo Symmetries}
}
Document
DOI: 10.4230/LIPIcs.SAT.2023.13
A SAT Solver’s Opinion on the Erdős-Faber-Lovász Conjecture

Authors: Markus Kirchweger, Tomáš Peitl, and Stefan Szeider

Published in: LIPIcs, Volume 271, 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)

Abstract
In 1972, Paul Erdős, Vance Faber, and Lászlo Lovász asked whether every linear hypergraph with n vertices can be edge-colored with n colors, a statement that has come to be known as the EFL conjecture. Erdős himself considered the conjecture as one of his three favorite open problems, and offered increasing money prizes for its solution on several occasions. A proof of the conjecture was recently announced, for all but a finite number of hypergraphs. In this paper we look at some of the cases not covered by this proof. We use SAT solvers, and in particular the SAT Modulo Symmetries (SMS) framework, to generate non-colorable linear hypergraphs with a fixed number of vertices and hyperedges modulo isomorphisms. Since hypergraph colorability is NP-hard, we cannot directly express in a propositional formula that we want only non-colorable hypergraphs. Instead, we use one SAT (SMS) solver to generate candidate hypergraphs modulo isomorphisms, and another to reject them by finding a coloring. Each successive candidate is required to defeat all previous colorings, whereby we avoid having to generate and test all linear hypergraphs. Computational methods have previously been used to verify the EFL conjecture for small hypergraphs. We verify and extend these results to larger values and discuss challenges and directions. Ours is the first computational approach to the EFL conjecture that allows producing independently verifiable, DRAT proofs.
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Markus Kirchweger, Tomáš Peitl, and Stefan Szeider. A SAT Solver’s Opinion on the Erdős-Faber-Lovász Conjecture. In 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 271, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{kirchweger_et_al:LIPIcs.SAT.2023.13,
  author =	{Kirchweger, Markus and Peitl, Tom\'{a}\v{s} and Szeider, Stefan},
  title =	{{A SAT Solver’s Opinion on the Erd\H{o}s-Faber-Lov\'{a}sz Conjecture}},
  booktitle =	{26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)},
  pages =	{13:1--13:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-286-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{271},
  editor =	{Mahajan, Meena and Slivovsky, Friedrich},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2023.13},
  URN =		{urn:nbn:de:0030-drops-184752},
  doi =		{10.4230/LIPIcs.SAT.2023.13},
  annote =	{Keywords: hypergraphs, graph coloring, SAT modulo symmetries}
}
Document
DOI: 10.4230/LIPIcs.SAT.2023.14
SAT-Based Generation of Planar Graphs

Authors: Markus Kirchweger, Manfred Scheucher, and Stefan Szeider

Published in: LIPIcs, Volume 271, 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)

Abstract
To test a graph’s planarity in SAT-based graph generation we develop SAT encodings with dynamic symmetry breaking as facilitated in the SAT modulo Symmetry (SMS) framework. We implement and compare encodings based on three planarity criteria. In particular, we consider two eager encodings utilizing order-based and universal-set-based planarity criteria, and a lazy encoding based on Kuratowski’s theorem. The performance and scalability of these encodings are compared on two prominent problems from combinatorics: the computation of planar Turán numbers and the Earth-Moon problem. We further showcase the power of SMS equipped with a planarity encoding by verifying and extending several integer sequences from the Online Encyclopedia of Integer Sequences (OEIS) related to planar graph enumeration. Furthermore, we extend the SMS framework to directed graphs which might be of independent interest.
Cite as

Markus Kirchweger, Manfred Scheucher, and Stefan Szeider. SAT-Based Generation of Planar Graphs. In 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 271, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{kirchweger_et_al:LIPIcs.SAT.2023.14,
  author =	{Kirchweger, Markus and Scheucher, Manfred and Szeider, Stefan},
  title =	{{SAT-Based Generation of Planar Graphs}},
  booktitle =	{26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)},
  pages =	{14:1--14:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-286-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{271},
  editor =	{Mahajan, Meena and Slivovsky, Friedrich},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2023.14},
  URN =		{urn:nbn:de:0030-drops-184767},
  doi =		{10.4230/LIPIcs.SAT.2023.14},
  annote =	{Keywords: SAT modulo Symmetry (SMS), dynamic symmetry breaking, planarity test, universal point set, order dimension, Schnyder’s theorem, Kuratowski’s theorem, Tur\'{a}n’s theorem, Earth-Moon problem}
}
Document
DOI: 10.4230/LIPIcs.SAT.2022.4
A SAT Attack on Rota’s Basis Conjecture

Authors: Markus Kirchweger, Manfred Scheucher, and Stefan Szeider

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

Abstract
The SAT modulo Symmetries (SMS) is a recently introduced framework for dynamic symmetry breaking in SAT instances. It combines a CDCL SAT solver with an external lexicographic minimality checking algorithm. We extend SMS from graphs to matroids and use it to progress on Rota’s Basis Conjecture (1989), which states that one can always decompose a collection of r disjoint bases of a rank r matroid into r disjoint rainbow bases. Through SMS, we establish that the conjecture holds for all matroids of rank 4 and certain special cases of matroids of rank 5. Furthermore, we extend SMS with the facility to produce DRAT proofs. External tools can then be used to verify the validity of additional axioms produced by the lexicographic minimality check. As a byproduct, we have utilized our framework to enumerate matroids modulo isomorphism and to support the investigation of various other problems on matroids.
Cite as

Markus Kirchweger, Manfred Scheucher, and Stefan Szeider. A SAT Attack on Rota’s Basis Conjecture. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 4:1-4:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kirchweger_et_al:LIPIcs.SAT.2022.4,
  author =	{Kirchweger, Markus and Scheucher, Manfred and Szeider, Stefan},
  title =	{{A SAT Attack on Rota’s Basis Conjecture}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{4:1--4:18},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2022.4},
  URN =		{urn:nbn:de:0030-drops-166780},
  doi =		{10.4230/LIPIcs.SAT.2022.4},
  annote =	{Keywords: SAT modulo Symmetry (SMS), dynamic symmetry breaking, Rota’s basis conjecture, matroid}
}
Document
DOI: 10.4230/LIPIcs.CP.2021.34
SAT Modulo Symmetries for Graph Generation

Authors: Markus Kirchweger and Stefan Szeider

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

Abstract
We propose a novel constraint-based approach to graph generation. Our approach utilizes the interaction between a CDCL SAT solver and a special symmetry propagator where the SAT solver runs on an encoding of the desired graph property. The symmetry propagator checks partially generated graphs for minimality w.r.t. a lexicographic ordering during the solving process. This approach has several advantages over a static symmetry breaking: (i) symmetries are detected early in the generation process, (ii) symmetry breaking is seamlessly integrated into the CDCL procedure, and (iii) the propagator can perform a complete symmetry breaking without causing a prohibitively large initial encoding. We instantiate our approach by generating extremal graphs with certain restrictions in terms of girth and diameter. With our approach, we could confirm the Simon-Murty Conjecture (1979) on diameter-2-critical graphs for graphs up to 18 vertices.
Cite as

Markus Kirchweger and Stefan Szeider. SAT Modulo Symmetries for Graph Generation. In 27th International Conference on Principles and Practice of Constraint Programming (CP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 210, pp. 34:1-34:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{kirchweger_et_al:LIPIcs.CP.2021.34,
  author =	{Kirchweger, Markus and Szeider, Stefan},
  title =	{{SAT Modulo Symmetries for Graph Generation}},
  booktitle =	{27th International Conference on Principles and Practice of Constraint Programming (CP 2021)},
  pages =	{34:1--34:16},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2021.34},
  URN =		{urn:nbn:de:0030-drops-153257},
  doi =		{10.4230/LIPIcs.CP.2021.34},
  annote =	{Keywords: symmetry breaking, SAT encodings, graph generation, combinatorial search, extremal graphs, CDCL}
}
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