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Documents authored by Heule, Marijn J. H.

Document
DOI: 10.4230/LIPIcs.ITP.2024.35
Formal Verification of the Empty Hexagon Number

Authors: Bernardo Subercaseaux, Wojciech Nawrocki, James Gallicchio, Cayden Codel, Mario Carneiro, and Marijn J. H. Heule

Published in: LIPIcs, Volume 309, 15th International Conference on Interactive Theorem Proving (ITP 2024)

Abstract
A recent breakthrough in computer-assisted mathematics showed that every set of 30 points in the plane in general position (i.e., no three points on a common line) contains an empty convex hexagon. Heule and Scheucher solved this problem with a combination of geometric insights and automated reasoning techniques by constructing CNF formulas ϕ_n, with O(n⁴) clauses, such that if ϕ_n is unsatisfiable then every set of n points in general position must contain an empty convex hexagon. An unsatisfiability proof for n = 30 was then found with a SAT solver using 17 300 CPU hours of parallel computation. In this paper, we formalize and verify this result in the Lean theorem prover. Our formalization covers ideas in discrete computational geometry and SAT encoding techniques by introducing a framework that connects geometric objects to propositional assignments. We see this as a key step towards the formal verification of other SAT-based results in geometry, since the abstractions we use have been successfully applied to similar problems. Overall, we hope that our work sets a new standard for the verification of geometry problems relying on extensive computation, and that it increases the trust the mathematical community places in computer-assisted proofs.
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Bernardo Subercaseaux, Wojciech Nawrocki, James Gallicchio, Cayden Codel, Mario Carneiro, and Marijn J. H. Heule. Formal Verification of the Empty Hexagon Number. In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 35:1-35:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{subercaseaux_et_al:LIPIcs.ITP.2024.35,
  author =	{Subercaseaux, Bernardo and Nawrocki, Wojciech and Gallicchio, James and Codel, Cayden and Carneiro, Mario and Heule, Marijn J. H.},
  title =	{{Formal Verification of the Empty Hexagon Number}},
  booktitle =	{15th International Conference on Interactive Theorem Proving (ITP 2024)},
  pages =	{35:1--35:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-337-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{309},
  editor =	{Bertot, Yves and Kutsia, Temur and Norrish, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2024.35},
  URN =		{urn:nbn:de:0030-drops-207633},
  doi =		{10.4230/LIPIcs.ITP.2024.35},
  annote =	{Keywords: Empty Hexagon Number, Discrete Computational Geometry, Erd\H{o}s-Szekeres}
}
Document
DOI: 10.4230/LIPIcs.SAT.2024.29
Quantum Circuit Mapping Based on Incremental and Parallel SAT Solving

Authors: Jiong Yang, Yaroslav A. Kharkov, Yunong Shi, Marijn J. H. Heule, and Bruno Dutertre

Published in: LIPIcs, Volume 305, 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)

Abstract
Quantum Computing (QC) is a new computational paradigm that promises significant speedup over classical computing in various domains. However, near-term QC faces numerous challenges, including limited qubit connectivity and noisy quantum operations. To address the qubit connectivity constraint, circuit mapping is required for executing quantum circuits on quantum computers. This process involves performing initial qubit placement and using the quantum SWAP operations to relocate non-adjacent qubits for nearest-neighbor interaction. Reducing the SWAP count in circuit mapping is essential for improving the success rate of quantum circuit execution as SWAPs are costly and error-prone. In this work, we introduce a novel circuit mapping method by combining incremental and parallel solving for Boolean Satisfiability (SAT). We present an innovative SAT encoding for circuit mapping problems, which significantly improves solver-based mapping methods and provides a smooth trade-off between compilation quality and compilation time. Through comprehensive benchmarking of 78 instances covering 3 quantum algorithms on 2 distinct quantum computer topologies, we demonstrate that our method is 26× faster than state-of-the-art solver-based methods, reducing the compilation time from hours to minutes for important quantum applications. Our method also surpasses the existing heuristics algorithm by 26% in SWAP count.
Cite as

Jiong Yang, Yaroslav A. Kharkov, Yunong Shi, Marijn J. H. Heule, and Bruno Dutertre. Quantum Circuit Mapping Based on Incremental and Parallel SAT Solving. In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 29:1-29:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{yang_et_al:LIPIcs.SAT.2024.29,
  author =	{Yang, Jiong and Kharkov, Yaroslav A. and Shi, Yunong and Heule, Marijn J. H. and Dutertre, Bruno},
  title =	{{Quantum Circuit Mapping Based on Incremental and Parallel SAT Solving}},
  booktitle =	{27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)},
  pages =	{29:1--29:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-334-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{305},
  editor =	{Chakraborty, Supratik and Jiang, Jie-Hong Roland},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2024.29},
  URN =		{urn:nbn:de:0030-drops-205517},
  doi =		{10.4230/LIPIcs.SAT.2024.29},
  annote =	{Keywords: Quantum computing, Quantum compilation, SAT solving, Incremental solving, Parallel solving}
}
Document
DOI: 10.4230/LIPIcs.FUN.2024.14
PackIt!: Gamified Rectangle Packing

Authors: Thomas Garrison, Marijn J. H. Heule, and Bernardo Subercaseaux

Published in: LIPIcs, Volume 291, 12th International Conference on Fun with Algorithms (FUN 2024)

Abstract
We present and analyze PackIt!, a turn-based game consisting of packing rectangles on an n × n grid. PackIt! can be easily played on paper, either as a competitive two-player game or in solitaire fashion. On the t-th turn, a rectangle of area t or t+1 must be placed in the grid. In the two-player format of PackIt! whichever player places a rectangle last wins, whereas the goal in the solitaire variant is to perfectly pack the n × n grid. We analyze necessary conditions for the existence of a perfect packing over n × n, then present an automated reasoning approach that allows finding perfect games of PackIt! up to n = 50 which includes a novel SAT-encoding technique of independent interest, and conclude by proving an NP-hardness result.
Cite as

Thomas Garrison, Marijn J. H. Heule, and Bernardo Subercaseaux. PackIt!: Gamified Rectangle Packing. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 14:1-14:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{garrison_et_al:LIPIcs.FUN.2024.14,
  author =	{Garrison, Thomas and Heule, Marijn J. H. and Subercaseaux, Bernardo},
  title =	{{PackIt!: Gamified Rectangle Packing}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{14:1--14:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-314-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{291},
  editor =	{Broder, Andrei Z. and Tamir, Tami},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2024.14},
  URN =		{urn:nbn:de:0030-drops-199226},
  doi =		{10.4230/LIPIcs.FUN.2024.14},
  annote =	{Keywords: PackIt!, rectangle packing, SAT, NP-hardness}
}
Document
DOI: 10.4230/DagRep.13.6.106
SAT Encodings and Beyond (Dagstuhl Seminar 23261)

Authors: Marijn J. H. Heule, Inês Lynce, Stefan Szeider, and Andre Schidler

Published in: Dagstuhl Reports, Volume 13, Issue 6 (2024)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 23261 "SAT Encodings and Beyond." The seminar facilitated an intense examination and discussion of current results and challenges related to encodings for SAT and related solving paradigms. The seminar featured presentations and group work that provided theoretical, practical, and industrial viewpoints. The goal was to foster more profound insights and advancements in encoding techniques, which are pivotal in enhancing solvers' efficiency.
Cite as

Marijn J. H. Heule, Inês Lynce, Stefan Szeider, and Andre Schidler. SAT Encodings and Beyond (Dagstuhl Seminar 23261). In Dagstuhl Reports, Volume 13, Issue 6, pp. 106-122, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{heule_et_al:DagRep.13.6.106,
  author =	{Heule, Marijn J. H. and Lynce, In\^{e}s and Szeider, Stefan and Schidler, Andre},
  title =	{{SAT Encodings and Beyond (Dagstuhl Seminar 23261)}},
  pages =	{106--122},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2024},
  volume =	{13},
  number =	{6},
  editor =	{Heule, Marijn J. H. and Lynce, In\^{e}s and Szeider, Stefan and Schidler, Andre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.6.106},
  URN =		{urn:nbn:de:0030-drops-196409},
  doi =		{10.4230/DagRep.13.6.106},
  annote =	{Keywords: constraint propagation, lower and upper bounds, problem formulation, propositional satisfiability, symmetry breaking}
}
Document
DOI: 10.4230/LIPIcs.SAT.2023.6
Certified Knowledge Compilation with Application to Verified Model Counting

Authors: Randal E. Bryant, Wojciech Nawrocki, Jeremy Avigad, and Marijn J. H. Heule

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

Abstract
Computing many useful properties of Boolean formulas, such as their weighted or unweighted model count, is intractable on general representations. It can become tractable when formulas are expressed in a special form, such as the decision-decomposable, negation normal form (dec-DNNF) . Knowledge compilation is the process of converting a formula into such a form. Unfortunately existing knowledge compilers provide no guarantee that their output correctly represents the original formula, and therefore they cannot validate a model count, or any other computed value. We present Partitioned-Operation Graphs (POGs), a form that can encode all of the representations used by existing knowledge compilers. We have designed CPOG, a framework that can express proofs of equivalence between a POG and a Boolean formula in conjunctive normal form (CNF). We have developed a program that generates POG representations from dec-DNNF graphs produced by the state-of-the-art knowledge compiler D4, as well as checkable CPOG proofs certifying that the output POGs are equivalent to the input CNF formulas. Our toolchain for generating and verifying POGs scales to all but the largest graphs produced by D4 for formulas from a recent model counting competition. Additionally, we have developed a formally verified CPOG checker and model counter for POGs in the Lean 4 proof assistant. In doing so, we proved the soundness of our proof framework. These programs comprise the first formally verified toolchain for weighted and unweighted model counting.
Cite as

Randal E. Bryant, Wojciech Nawrocki, Jeremy Avigad, and Marijn J. H. Heule. Certified Knowledge Compilation with Application to Verified Model Counting. In 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 271, pp. 6:1-6:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bryant_et_al:LIPIcs.SAT.2023.6,
  author =	{Bryant, Randal E. and Nawrocki, Wojciech and Avigad, Jeremy and Heule, Marijn J. H.},
  title =	{{Certified Knowledge Compilation with Application to Verified Model Counting}},
  booktitle =	{26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)},
  pages =	{6:1--6:20},
  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.2023.6},
  URN =		{urn:nbn:de:0030-drops-184685},
  doi =		{10.4230/LIPIcs.SAT.2023.6},
  annote =	{Keywords: Propositional model counting, Proof checking}
}
Document
DOI: 10.4230/LIPIcs.SAT.2023.11
Effective Auxiliary Variables via Structured Reencoding

Authors: Andrew Haberlandt, Harrison Green, and Marijn J. H. Heule

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

Abstract
Extended resolution shows that auxiliary variables are very powerful in theory. However, attempts to exploit this potential in practice have had limited success. One reasonably effective method in this regard is bounded variable addition (BVA), which automatically reencodes formulas by introducing new variables and eliminating clauses, often significantly reducing formula size. We find motivating examples suggesting that the performance improvement caused by BVA stems not only from this size reduction but also from the introduction of effective auxiliary variables. Analyzing specific packing-coloring instances, we discover that BVA is fragile with respect to formula randomization, relying on variable order to break ties. With this understanding, we augment BVA with a heuristic for breaking ties in a structured way. We evaluate our new preprocessing technique, Structured BVA (SBVA), on more than 29 000 formulas from previous SAT competitions and show that it is robust to randomization. In a simulated competition setting, our implementation outperforms BVA on both randomized and original formulas, and appears to be well-suited for certain families of formulas.
Cite as

Andrew Haberlandt, Harrison Green, and Marijn J. H. Heule. Effective Auxiliary Variables via Structured Reencoding. In 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 271, pp. 11:1-11:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{haberlandt_et_al:LIPIcs.SAT.2023.11,
  author =	{Haberlandt, Andrew and Green, Harrison and Heule, Marijn J. H.},
  title =	{{Effective Auxiliary Variables via Structured Reencoding}},
  booktitle =	{26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)},
  pages =	{11:1--11:19},
  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.2023.11},
  URN =		{urn:nbn:de:0030-drops-184736},
  doi =		{10.4230/LIPIcs.SAT.2023.11},
  annote =	{Keywords: Reencoding, Auxiliary Variables, Extended Resolution}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.101
Exponential Separations Using Guarded Extension Variables

Authors: Emre Yolcu and Marijn J. H. Heule

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
We study the complexity of proof systems augmenting resolution with inference rules that allow, given a formula Γ in conjunctive normal form, deriving clauses that are not necessarily logically implied by Γ but whose addition to Γ preserves satisfiability. When the derived clauses are allowed to introduce variables not occurring in Γ, the systems we consider become equivalent to extended resolution. We are concerned with the versions of these systems without new variables. They are called BC⁻, RAT⁻, SBC⁻, and GER⁻, denoting respectively blocked clauses, resolution asymmetric tautologies, set-blocked clauses, and generalized extended resolution. Each of these systems formalizes some restricted version of the ability to make assumptions that hold "without loss of generality," which is commonly used informally to simplify or shorten proofs. Except for SBC⁻, these systems are known to be exponentially weaker than extended resolution. They are, however, all equivalent to it under a relaxed notion of simulation that allows the translation of the formula along with the proof when moving between proof systems. By taking advantage of this fact, we construct formulas that separate RAT⁻ from GER⁻ and vice versa. With the same strategy, we also separate SBC⁻ from RAT⁻. Additionally, we give polynomial-size SBC⁻ proofs of the pigeonhole principle, which separates SBC⁻ from GER⁻ by a previously known lower bound. These results also separate the three systems from BC⁻ since they all simulate it. We thus give an almost complete picture of their relative strengths.
Cite as

Emre Yolcu and Marijn J. H. Heule. Exponential Separations Using Guarded Extension Variables. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 101:1-101:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{yolcu_et_al:LIPIcs.ITCS.2023.101,
  author =	{Yolcu, Emre and Heule, Marijn J. H.},
  title =	{{Exponential Separations Using Guarded Extension Variables}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{101:1--101:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.101},
  URN =		{urn:nbn:de:0030-drops-176043},
  doi =		{10.4230/LIPIcs.ITCS.2023.101},
  annote =	{Keywords: proof complexity, separations, resolution, extended resolution, blocked clauses}
}
Document
DOI: 10.4230/LIPIcs.SAT.2022.10
Relating Existing Powerful Proof Systems for QBF

Authors: Leroy Chew and Marijn J. H. Heule

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

Abstract
We advance the theory of QBF proof systems by showing the first simulation of the universal checking format QRAT by a theory-friendly system. We show that the sequent system G fully p-simulates QRAT, including the Extended Universal Reduction (EUR) rule which was recently used to show QRAT does not have strategy extraction. Because EUR heavily uses resolution paths our technique also brings resolution path dependency and sequent systems closer together. While we do not recommend G for practical applications this work can potentially show what features are needed for a new QBF checking format stronger than QRAT.
Cite as

Leroy Chew and Marijn J. H. Heule. Relating Existing Powerful Proof Systems for QBF. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 10:1-10:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chew_et_al:LIPIcs.SAT.2022.10,
  author =	{Chew, Leroy and Heule, Marijn J. H.},
  title =	{{Relating Existing Powerful Proof Systems for QBF}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{10:1--10:22},
  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.2022.10},
  URN =		{urn:nbn:de:0030-drops-166845},
  doi =		{10.4230/LIPIcs.SAT.2022.10},
  annote =	{Keywords: QBF, Proof Complexity, Verification, Strategy Extraction, Sequent Calculus}
}
Document
DOI: 10.4230/LIPIcs.SAT.2022.27
Migrating Solver State

Authors: Armin Biere, Md Solimul Chowdhury, Marijn J. H. Heule, Benjamin Kiesl, and Michael W. Whalen

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

Abstract
We present approaches to store and restore the state of a SAT solver, allowing us to migrate the state between different compute resources, or even between different solvers. This can be used in many ways, e.g., to improve the fault tolerance of solvers, to schedule SAT problems on a restricted number of cores, or to use dedicated preprocessing tools for inprocessing. We identify a minimum viable subset of the solver state to migrate such that the loss of performance is small. We then present and implement two different approaches to state migration: one approach stores the state at the end of a solver run whereas the other approach stores the state continuously as part of the proof trace. We show that our approaches enable the generation of correct models and valid unsatisfiability proofs. Experimental results confirm that the overhead is reasonable and that in several cases solver performance actually improves.
Cite as

Armin Biere, Md Solimul Chowdhury, Marijn J. H. Heule, Benjamin Kiesl, and Michael W. Whalen. Migrating Solver State. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 27:1-27:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{biere_et_al:LIPIcs.SAT.2022.27,
  author =	{Biere, Armin and Chowdhury, Md Solimul and Heule, Marijn J. H. and Kiesl, Benjamin and Whalen, Michael W.},
  title =	{{Migrating Solver State}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{27:1--27:24},
  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.2022.27},
  URN =		{urn:nbn:de:0030-drops-167015},
  doi =		{10.4230/LIPIcs.SAT.2022.27},
  annote =	{Keywords: SAT, SMT, Cloud Computing, Serverless Computing}
}
Document
DOI: 10.4230/LIPIcs.CP.2022.26
From Cliques to Colorings and Back Again

Authors: Marijn J. H. Heule, Anthony Karahalios, and Willem-Jan van Hoeve

Published in: LIPIcs, Volume 235, 28th International Conference on Principles and Practice of Constraint Programming (CP 2022)

Abstract
We present an exact algorithm for graph coloring and maximum clique problems based on SAT technology. It relies on four sub-algorithms that alternatingly compute cliques of larger size and colorings with fewer colors. We show how these techniques can mutually help each other: larger cliques facilitate finding smaller colorings, which in turn can boost finding larger cliques. We evaluate our approach on the DIMACS graph coloring suite. For finding maximum cliques, we show that our algorithm can improve the state-of-the-art MaxSAT-based solver IncMaxCLQ, and for the graph coloring problem, we close two open instances, decrease two upper bounds, and increase one lower bound.
Cite as

Marijn J. H. Heule, Anthony Karahalios, and Willem-Jan van Hoeve. From Cliques to Colorings and Back Again. In 28th International Conference on Principles and Practice of Constraint Programming (CP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 235, pp. 26:1-26:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{heule_et_al:LIPIcs.CP.2022.26,
  author =	{Heule, Marijn J. H. and Karahalios, Anthony and van Hoeve, Willem-Jan},
  title =	{{From Cliques to Colorings and Back Again}},
  booktitle =	{28th International Conference on Principles and Practice of Constraint Programming (CP 2022)},
  pages =	{26:1--26:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-240-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{235},
  editor =	{Solnon, Christine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2022.26},
  URN =		{urn:nbn:de:0030-drops-166558},
  doi =		{10.4230/LIPIcs.CP.2022.26},
  annote =	{Keywords: Graph coloring, maximum clique, Boolean satisfiability}
}
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