15 Search Results for "Kirchweger, Markus"

Document
DOI: 10.4230/LIPIcs.CP.2026.33
Smart Cubing for Graph Search: A Comparative Study

Authors: Markus Kirchweger, Tomáš Peitl, Stefan Szeider, and Hai Xia

Published in: LIPIcs, Volume 379, 32nd International Conference on Principles and Practice of Constraint Programming (CP 2026)

Abstract
Parallel solving via cube-and-conquer is a key method for solving hard instances with SAT. While cube-and-conquer has proven successful for pure SAT problems, notably the Pythagorean triples conjecture, its application to SAT solvers augmented with propagators presents unique challenges as propagators learn constraints dynamically during the search. We study this problem using SAT Modulo Symmetries (SMS) as our primary test case. In our setting, the SMS symmetry-breaking propagator is an ordinary IPASIR-UP propagator; the techniques below do not rely on properties specific to symmetry breaking, except in the benchmark instantiations. Through extensive experimentation comprising over 20,000 CPU hours, we systematically evaluate different cube-and-conquer variants on three well-studied combinatorial problems. Our methodology combines prerun phases to collect learned constraints, various cubing strategies, and parameter tuning via algorithm configuration. The comprehensive empirical evaluation provides new insights into effective cubing strategies for propagator-based SAT solving. Our best method reduces total solving time by factors of 2-10x from improved cubing, and reduces the time for the hardest cubes by factors of 2-50x.
Cite as

Markus Kirchweger, Tomáš Peitl, Stefan Szeider, and Hai Xia. Smart Cubing for Graph Search: A Comparative Study. In 32nd International Conference on Principles and Practice of Constraint Programming (CP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 379, pp. 33:1-33:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kirchweger_et_al:LIPIcs.CP.2026.33,
  author =	{Kirchweger, Markus and Peitl, Tom\'{a}\v{s} and Szeider, Stefan and Xia, Hai},
  title =	{{Smart Cubing for Graph Search: A Comparative Study}},
  booktitle =	{32nd International Conference on Principles and Practice of Constraint Programming (CP 2026)},
  pages =	{33:1--33:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-432-1},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{379},
  editor =	{Beldiceanu, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2026.33},
  URN =		{urn:nbn:de:0030-drops-266652},
  doi =		{10.4230/LIPIcs.CP.2026.33},
  annote =	{Keywords: cube and conquer, graph search, algorithm configuration, SAT solving}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.15
Symmetry Classes of Hamiltonian Cycles

Authors: Júlia Baligács, Sofia Brenner, Annette Lutz, and Lena Volk

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
We initiate the study of Hamiltonian cycles up to symmetries of the underlying graph. Our focus lies on the extremal case of Hamiltonian-transitive graphs, i.e., Hamiltonian graphs where, for every pair of Hamiltonian cycles, there is a graph automorphism mapping one cycle to the other. This generalizes the extensively studied uniquely Hamiltonian graphs. In this paper, we show that Cayley graphs of abelian groups are not Hamiltonian-transitive (under some mild conditions and some non-surprising exceptions), i.e., they contain at least two structurally different Hamiltonian cycles. To show this, we reduce Hamiltonian-transitivity to properties of the prime factors of a Cartesian product decomposition, which we believe is interesting in its own right. We complement our results by constructing infinite families of regular Hamiltonian-transitive graphs and take a look at the opposite extremal case by constructing a family with many different Hamiltonian cycles up to symmetry.
Cite as

Júlia Baligács, Sofia Brenner, Annette Lutz, and Lena Volk. Symmetry Classes of Hamiltonian Cycles. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{baligacs_et_al:LIPIcs.MFCS.2025.15,
  author =	{Balig\'{a}cs, J\'{u}lia and Brenner, Sofia and Lutz, Annette and Volk, Lena},
  title =	{{Symmetry Classes of Hamiltonian Cycles}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{15:1--15:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.15},
  URN =		{urn:nbn:de:0030-drops-241221},
  doi =		{10.4230/LIPIcs.MFCS.2025.15},
  annote =	{Keywords: Hamiltonian cycles, graph automorphisms, Cayley graphs, abelian groups, Cartesian product of graphs}
}
Document
Short Paper
DOI: 10.4230/LIPIcs.CP.2025.42
Towards Modern and Modular SAT for LCG (Short Paper)

Authors: Jip J. Dekker, Alexey Ignatiev, Peter J. Stuckey, and Allen Z. Zhong

Published in: LIPIcs, Volume 340, 31st International Conference on Principles and Practice of Constraint Programming (CP 2025)

Abstract
Lazy Clause Generation (LCG) is an architecture for building Constraint Programming (CP) solvers using an underlying Boolean Satisfiability (SAT) engine. The CP propagation engine lazily creates clauses that define the integer variables and impose problem restrictions. The SAT engine uses the clausal model to reason and search, including, crucially, the generation of nogoods. However, while SAT solving has made significant advances recently, the underlying SAT technology in most LCG solvers has largely remained the same. Using a new interface to SAT engines, IPASIR-UP, we can construct an LCG solver which can swap out the underlying SAT engine with any that supports the interface. This new approach means we need to revisit many of the design and engineering decisions for LCG solvers, to take maximum advantage of a better underlying SAT engine while adhering to the restrictions of the interface. In this paper, we explore the possibilities and challenges of using IPASIR-UP for LCG, showing that it can be used to create a highly competitive solver.
Cite as

Jip J. Dekker, Alexey Ignatiev, Peter J. Stuckey, and Allen Z. Zhong. Towards Modern and Modular SAT for LCG (Short Paper). In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 42:1-42:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dekker_et_al:LIPIcs.CP.2025.42,
  author =	{Dekker, Jip J. and Ignatiev, Alexey and Stuckey, Peter J. and Zhong, Allen Z.},
  title =	{{Towards Modern and Modular SAT for LCG}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{42:1--42:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-380-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{340},
  editor =	{de la Banda, Maria Garcia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2025.42},
  URN =		{urn:nbn:de:0030-drops-239038},
  doi =		{10.4230/LIPIcs.CP.2025.42},
  annote =	{Keywords: Lazy Clause Generation, Boolean Satisfiability, IPASIR-UP}
}
Document
DOI: 10.4230/LIPIcs.CP.2025.39
The 3-Decomposition Conjecture: A SAT-Based Approach with Specialized Propagators

Authors: Tianwei Zhang and Stefan Szeider

Published in: LIPIcs, Volume 340, 31st International Conference on Principles and Practice of Constraint Programming (CP 2025)

Abstract
We investigate the 3-decomposition conjecture, which states that every connected cubic graph can be decomposed into a spanning tree, a collection of cycles, and a matching. Using a SAT-based approach enhanced with specialized propagators, we verify the conjecture for all relevant graphs up to 28 vertices. Our method extends the Satisfiability Modulo Symmetries (SMS) framework with specialized propagators that exploit theoretical properties of minimal counterexamples (counterexamples with the minimal number of vertices), enabling efficient pruning. We demonstrate that graphs containing certain substructures cannot be minimal counterexamples to the conjecture, allowing us to exclude these patterns during the search dynamically. Our experimental results quantify the impact of different propagator configurations and forbidden subgraph constraints on solving efficiency, showing significant performance improvements when leveraging these techniques. The approach scales effectively to graphs of 28 vertices. Our work illustrates how combining SAT solving with specialized constraint propagation techniques can successfully address challenging combinatorial problems in contemporary graph theory.
Cite as

Tianwei Zhang and Stefan Szeider. The 3-Decomposition Conjecture: A SAT-Based Approach with Specialized Propagators. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 39:1-39:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zhang_et_al:LIPIcs.CP.2025.39,
  author =	{Zhang, Tianwei and Szeider, Stefan},
  title =	{{The 3-Decomposition Conjecture: A SAT-Based Approach with Specialized Propagators}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{39:1--39:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-380-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{340},
  editor =	{de la Banda, Maria Garcia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2025.39},
  URN =		{urn:nbn:de:0030-drops-239005},
  doi =		{10.4230/LIPIcs.CP.2025.39},
  annote =	{Keywords: SAT, Symmetry Breaking, Subgraphs, Propagators, Combinatorics}
}
Document
DOI: 10.4230/LIPIcs.CP.2025.8
Breaking Symmetries with Involutions

Authors: Michael Codish and Mikoláš Janota

Published in: LIPIcs, Volume 340, 31st International Conference on Principles and Practice of Constraint Programming (CP 2025)

Abstract
Symmetry breaking for graphs and other combinatorial objects is notoriously hard. On the one hand, complete symmetry breaks are exponential in size. On the other hand, current, state-of-the-art, partial symmetry breaks are often considered too weak to be of practical use. Recently, the concept of graph patterns has been introduced and provides a concise representation for (large) sets of non-canonical graphs, i.e. graphs that are not lex-leaders and can be excluded from search. In particular, four (specific) graph patterns apply to identify about 3/4 of the set of all non-canonical graphs. Taking this approach further, we discover that graph patterns that derive from permutations that are involutions play an important role in the construction of symmetry breaks for graphs. We take advantage of this to guide the construction of partial and complete symmetry-breaking constraints based on graph patterns. The resulting constraints are small in size and strong in the number of symmetries they break.
Cite as

Michael Codish and Mikoláš Janota. Breaking Symmetries with Involutions. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{codish_et_al:LIPIcs.CP.2025.8,
  author =	{Codish, Michael and Janota, Mikol\'{a}\v{s}},
  title =	{{Breaking Symmetries with Involutions}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{8:1--8:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-380-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{340},
  editor =	{de la Banda, Maria Garcia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2025.8},
  URN =		{urn:nbn:de:0030-drops-238699},
  doi =		{10.4230/LIPIcs.CP.2025.8},
  annote =	{Keywords: graph symmetry, patterns, permutation, Ramsey graphs, greedy, CEGAR}
}
Document
DOI: 10.4230/LIPIcs.CP.2025.15
Symmetric Core Learning for Pseudo-Boolean Optimization by Implicit Hitting Sets

Authors: Hannes Ihalainen, Jeremias Berg, Matti Järvisalo, and Bart Bogaerts

Published in: LIPIcs, Volume 340, 31st International Conference on Principles and Practice of Constraint Programming (CP 2025)

Abstract
We propose symmetric core learning (SCL) as a novel approach to making the implicit hitting set approach (IHS) to constraint optimization more symmetry-aware. SCL has the potential of significantly reducing the number of iterations and, in particular, the number of calls to an NP decision solver for extracting individual unsatisfiable cores. As the technique is focused on generating symmetric cores to the hitting set component of IHS, SCL is generally applicable in IHS-style search for essentially any constraint optimization paradigm. In this work, we focus in particular on integrating SCL to IHS for pseudo-Boolean optimization (PBO), as earlier proposed static symmetry breaking through lex-leader constraints generated before search turns out to often degrade the performance of the IHS approach to PBO. In contrast, we show that SCL can improve the runtime performance of a state-of-the-art IHS approach to PBO and generally does not impose significant overhead in terms of runtime performance.
Cite as

Hannes Ihalainen, Jeremias Berg, Matti Järvisalo, and Bart Bogaerts. Symmetric Core Learning for Pseudo-Boolean Optimization by Implicit Hitting Sets. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 15:1-15:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ihalainen_et_al:LIPIcs.CP.2025.15,
  author =	{Ihalainen, Hannes and Berg, Jeremias and J\"{a}rvisalo, Matti and Bogaerts, Bart},
  title =	{{Symmetric Core Learning for Pseudo-Boolean Optimization by Implicit Hitting Sets}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{15:1--15:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-380-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{340},
  editor =	{de la Banda, Maria Garcia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2025.15},
  URN =		{urn:nbn:de:0030-drops-238767},
  doi =		{10.4230/LIPIcs.CP.2025.15},
  annote =	{Keywords: Implicit hitting sets, symmetries, unsatisfiable cores, pseudo-Boolean optimization}
}
Document
DOI: 10.4230/LIPIcs.CP.2025.32
BFS-Based Canonical Codes for Generating Graphs with Constraint Programming

Authors: Xiao Peng and Christine Solnon

Published in: LIPIcs, Volume 340, 31st International Conference on Principles and Practice of Constraint Programming (CP 2025)

Abstract
We consider the problem of generating all graphs that satisfy some given additional constraints (on vertex degrees, or cycle lengths, for example). Most previous works have proposed to generate canonical codes associated with adjacency matrices. In this paper, we consider canonical codes based on Breadth First Search (BFS), and we show how to generate them with Constraint Programming (CP): we introduce a set of basic constraints that must be satisfied by all canonical codes, thus breaking many symmetries, and we introduce a global constraint to break other symmetries. We illustrate the interest of our approach on connected claw-free cubic graphs, and show that it outperforms state-of-the-art CP and SAT Modulo Theory (SMT) approaches.
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Xiao Peng and Christine Solnon. BFS-Based Canonical Codes for Generating Graphs with Constraint Programming. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 32:1-32:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{peng_et_al:LIPIcs.CP.2025.32,
  author =	{Peng, Xiao and Solnon, Christine},
  title =	{{BFS-Based Canonical Codes for Generating Graphs with Constraint Programming}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{32:1--32:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-380-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{340},
  editor =	{de la Banda, Maria Garcia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2025.32},
  URN =		{urn:nbn:de:0030-drops-238935},
  doi =		{10.4230/LIPIcs.CP.2025.32},
  annote =	{Keywords: Graph Generation, Automorphisms, Symmetry Breaking}
}
Document
DOI: 10.4230/LIPIcs.SAT.2025.24
SAT-Based CEGAR Method for the Hamiltonian Cycle Problem Enhanced by Cut-Set Constraints

Authors: Ryoga Ohashi, Takehide Soh, Daniel Le Berre, Hidetomo Nabeshima, Mutsunori Banbara, Katsumi Inoue, and Naoyuki Tamura

Published in: LIPIcs, Volume 341, 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)

Abstract
In this paper, we propose an enhancement to the SAT-based counterexample-guided abstraction refinement (CEGAR) approach for solving the Hamiltonian Cycle Problem (HCP). Many SAT-based methods for HCP have been proposed, including a CEGAR-based method that repeatedly solves a relaxed version of HCP strengthened by counterexamples. However, when the counterexample space - represented by the full set of subcycle partitions - is large, it becomes difficult to find a solution. To address this, we introduce cut-set constraints in the refinement step, replacing traditional subcycle blocking constraints. Our evaluation shows that these cut-set constraints achieve equal or better reduction in the counterexample space, making it easier to find valid solutions. We further assessed performance using all 1001 instances from the FHCP challenge set and confirmed that the proposed method solved 937 instances within 1800 seconds, outperforming both the existing eager and CEGAR encodings (which solved at most 666 instances). This demonstrates the effectiveness of incorporating cut-set constraints into SAT-based CEGAR approaches.
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Ryoga Ohashi, Takehide Soh, Daniel Le Berre, Hidetomo Nabeshima, Mutsunori Banbara, Katsumi Inoue, and Naoyuki Tamura. SAT-Based CEGAR Method for the Hamiltonian Cycle Problem Enhanced by Cut-Set Constraints. In 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 341, pp. 24:1-24:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ohashi_et_al:LIPIcs.SAT.2025.24,
  author =	{Ohashi, Ryoga and Soh, Takehide and Le Berre, Daniel and Nabeshima, Hidetomo and Banbara, Mutsunori and Inoue, Katsumi and Tamura, Naoyuki},
  title =	{{SAT-Based CEGAR Method for the Hamiltonian Cycle Problem Enhanced by Cut-Set Constraints}},
  booktitle =	{28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)},
  pages =	{24:1--24:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-381-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{341},
  editor =	{Berg, Jeremias and Nordstr\"{o}m, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2025.24},
  URN =		{urn:nbn:de:0030-drops-237585},
  doi =		{10.4230/LIPIcs.SAT.2025.24},
  annote =	{Keywords: Hamiltonian Cycle Problem, SAT Encoding, CEGAR}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.85
Towards the Proximity Conjecture on Group-Labeled Matroids

Authors: Dániel Garamvölgyi, Ryuhei Mizutani, Taihei Oki, Tamás Schwarcz, and Yutaro Yamaguchi

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
Consider a matroid M whose ground set is equipped with a labeling to an abelian group. A basis of M is called F-avoiding if the sum of the labels of its elements is not in a forbidden label set F. Hörsch, Imolay, Mizutani, Oki, and Schwarcz (2024) conjectured that if an F-avoiding basis exists, then any basis can be transformed into an F-avoiding basis by exchanging at most |F| elements. This proximity conjecture is known to hold for certain specific groups; in the case where |F| ≤ 2; or when the matroid is subsequence-interchangeably base orderable (SIBO), which is a weakening of the so-called strongly base orderable (SBO) property. In this paper, we settle the proximity conjecture for sparse paving matroids or in the case where |F| ≤ 4. Related to the latter result, we present the first known example of a non-SIBO matroid. We further address the setting of multiple group-label constraints, showing proximity results for the cases of two labelings, SIBO matroids, matroids representable over a fixed, finite field, and sparse paving matroids.
Cite as

Dániel Garamvölgyi, Ryuhei Mizutani, Taihei Oki, Tamás Schwarcz, and Yutaro Yamaguchi. Towards the Proximity Conjecture on Group-Labeled Matroids. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 85:1-85:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{garamvolgyi_et_al:LIPIcs.ICALP.2025.85,
  author =	{Garamv\"{o}lgyi, D\'{a}niel and Mizutani, Ryuhei and Oki, Taihei and Schwarcz, Tam\'{a}s and Yamaguchi, Yutaro},
  title =	{{Towards the Proximity Conjecture on Group-Labeled Matroids}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{85:1--85:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.85},
  URN =		{urn:nbn:de:0030-drops-234628},
  doi =		{10.4230/LIPIcs.ICALP.2025.85},
  annote =	{Keywords: sparse paving matroid, subsequence-interchangeable base orderability, congruency constraint, multiple labelings}
}
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.
Cite as

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.
Cite as

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.
Cite as

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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