27 Search Results for "Creignou, Nadia"

Document
DOI: 10.4230/LIPIcs.STACS.2026.22
Modular Counting over 3-Element and Conservative Domains

Authors: Andrei A. Bulatov and Amirhossein Kazeminia

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
In the Constraint Satisfaction Problem (CSP for short) the goal is to decide the existence of a homomorphism from a given relational structure {G} to a given relational structure {H}. If the structure {H} is fixed and {G} is the only input, the problem is denoted CSP({H}). In its counting version, #CSP({H}), the task is to find the number of such homomorphisms. The CSP and #CSP have been used to model a wide variety of combinatorial problems and have received a tremendous amount of attention from researchers from multiple disciplines. In this paper we consider the modular version of the counting CSPs, that is, problems of the form #_pCSP({H}) of counting the number of homomorphisms to {H} modulo a fixed prime number p. Modular counting has been intensively studied during the last decade, although mainly in the case of graph homomorphisms. Here we continue the program of systematic research of modular counting of homomorphisms to general relational structures. The main results of the paper include a new way of reducing modular counting problems to smaller domains and a study of the complexity of such problems over 3-element domains and over conservative domains, that is, relational structures that allow to express (in a certain exact way) every possible unary predicate.
Cite as

Andrei A. Bulatov and Amirhossein Kazeminia. Modular Counting over 3-Element and Conservative Domains. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 22:1-22:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bulatov_et_al:LIPIcs.STACS.2026.22,
  author =	{Bulatov, Andrei A. and Kazeminia, Amirhossein},
  title =	{{Modular Counting over 3-Element and Conservative Domains}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{22:1--22:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.22},
  URN =		{urn:nbn:de:0030-drops-255114},
  doi =		{10.4230/LIPIcs.STACS.2026.22},
  annote =	{Keywords: Constraint Satisfaction Problem, Modular Counting}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.18
Bridging Treewidth and Clique-Width via Cograph-Modular-Treewidth

Authors: Václav Blažej, Satyabrata Jana, M. S. Ramanujan, and Peter Strulo

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
Many classical graph problems - such as Max Cut, Chromatic Number, Edge Dominating Set, and Hamiltonian Cycle - are polynomial-time solvable on cographs, fixed-parameter tractable (FPT) when parameterized by treewidth, but W[1]-hard when parameterized by clique-width. In contrast, Graph Isomorphism is FPT parameterized by treewidth, but for clique-width it is known to be in XP; whether it is FPT or W[1]-hard is open. This reveals a sharp tractability gap between treewidth and clique-width. In this work, we propose a new structural graph parameter, 𝒞-modular-treewidth, which lies between treewidth and clique-width. The parameter leverages modular decomposition and restricts modules to induce graphs from a fixed class 𝒞 (e.g., cographs or edgeless graphs). By exploiting true and false twins - a hallmark of cograph-like structure - our parameter allows the design of efficient algorithms for several hard problems beyond the reach of treewidth-based methods. In this work, we show that 𝒞-modular-treewidth enables efficient solutions under suitable choices of 𝒞, opening a new pathway in the parameterized complexity landscape between treewidth and clique-width. In particular we show that - When parameterized by cograph-modular-treewidth, Isomorphism admits an FPT algorithm, whereas Chromatic Number remains W[1]-hard. - When parameterized by independent-modular-treewidth, Hamiltonian Cycle and Edge Dominating Set remain W[1]-hard.
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Václav Blažej, Satyabrata Jana, M. S. Ramanujan, and Peter Strulo. Bridging Treewidth and Clique-Width via Cograph-Modular-Treewidth. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{blazej_et_al:LIPIcs.IPEC.2025.18,
  author =	{Bla\v{z}ej, V\'{a}clav and Jana, Satyabrata and Ramanujan, M. S. and Strulo, Peter},
  title =	{{Bridging Treewidth and Clique-Width via Cograph-Modular-Treewidth}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{18:1--18:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.18},
  URN =		{urn:nbn:de:0030-drops-251507},
  doi =		{10.4230/LIPIcs.IPEC.2025.18},
  annote =	{Keywords: Treewidth, Clique-width, Cograph, FPT, W\lbrack1\rbrack-hard}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.23
Enumeration Kernels for Vertex Cover and Feedback Vertex Set

Authors: Marin Bougeret, Guilherme C. M. Gomes, Vinicius F. dos Santos, and Ignasi Sau

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
Enumerative kernelization is a recent and promising area sitting at the intersection of parameterized complexity and enumeration algorithms. Its study began with the paper of Creignou et al. [Theory Comput. Syst., 2017], and development in the area has started to accelerate with the work of Golovach et al. [J. Comput. Syst. Sci., 2022]. The latter introduced polynomial-delay enumeration kernels and applied them in the study of structural parameterizations of the Matching Cut problem and some variants. Few other results, mostly on Longest Path and some generalizations of Matching Cut, have also been developed. However, little success has been seen in enumeration versions of Vertex Cover and Feedback Vertex Set, some of the most studied problems in kernelization. In this paper, we address this shortcoming. Our first result is a polynomial-delay enumeration kernel with 2k vertices for Enum Vertex Cover, where we wish to list all solutions with at most k vertices. This is obtained by developing a non-trivial lifting algorithm for the classical crown decomposition reduction rule, and directly improves upon the kernel with 𝒪(k²) vertices derived from the work of Creignou et al. Our other result is a polynomial-delay enumeration kernel with 𝒪(k³) vertices and edges for Enum Feedback Vertex Set; the proof is inspired by some ideas of Thomassé [TALG, 2010], but with a weaker bound on the kernel size due to difficulties in applying the q-expansion technique.
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Marin Bougeret, Guilherme C. M. Gomes, Vinicius F. dos Santos, and Ignasi Sau. Enumeration Kernels for Vertex Cover and Feedback Vertex Set. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bougeret_et_al:LIPIcs.IPEC.2025.23,
  author =	{Bougeret, Marin and C. M. Gomes, Guilherme and dos Santos, Vinicius F. and Sau, Ignasi},
  title =	{{Enumeration Kernels for Vertex Cover and Feedback Vertex Set}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{23:1--23:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.23},
  URN =		{urn:nbn:de:0030-drops-251552},
  doi =		{10.4230/LIPIcs.IPEC.2025.23},
  annote =	{Keywords: Kernelization, Enumeration, Vertex cover, Crown decomposition, Feedback vertex set}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.50
Matchgate Signatures Under Variable Permutations

Authors: Boning Meng and Yicheng Pan

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
In this work, we introduce the concept of permutable matchgate signatures and leverage it to establish dichotomy theorems for #CSP and #R_D-CSP (D ≥ 3) on planar graphs without the variable ordering restriction. We also present a complete characterization of permutable matchgate signatures and their relationship to symmetric signatures. Besides, we give a sufficient and necessary condition for determining whether a matchgate signature retains its property under a certain variable permutation, which can be checked in polynomial time. In addition, we prove a dichotomy for Pl-#R_D-CSP (D ≥ 3), where the variable ordering restriction exists.
Cite as

Boning Meng and Yicheng Pan. Matchgate Signatures Under Variable Permutations. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 50:1-50:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{meng_et_al:LIPIcs.ISAAC.2025.50,
  author =	{Meng, Boning and Pan, Yicheng},
  title =	{{Matchgate Signatures Under Variable Permutations}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{50:1--50:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.50},
  URN =		{urn:nbn:de:0030-drops-249587},
  doi =		{10.4230/LIPIcs.ISAAC.2025.50},
  annote =	{Keywords: Computational Complexity, Matchgate Signature, Counting CSP}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.11
Courcelle’s Theorem for Lipschitz Continuity

Authors: Tatsuya Gima, Soh Kumabe, and Yuichi Yoshida

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Lipschitz continuity of algorithms, introduced by Kumabe and Yoshida (FOCS'23), measures the stability of an algorithm against small input perturbations. Algorithms with small Lipschitz continuity are desirable, as they ensure reliable decision-making and reproducible scientific research. Several studies have proposed Lipschitz continuous algorithms for various combinatorial optimization problems, but these algorithms are problem-specific, requiring a separate design for each problem. To address this issue, we provide the first algorithmic meta-theorem in the field of Lipschitz continuous algorithms. Our result can be seen as a Lipschitz continuous analogue of Courcelle’s theorem, which offers Lipschitz continuous algorithms for problems on bounded-treewidth graphs. Specifically, we consider the problem of finding a vertex set in a graph that maximizes or minimizes the total weight, subject to constraints expressed in monadic second-order logic (MSO₂). We show that for any ε > 0, there exists a (1±ε)-approximation algorithm for the problem with a polylogarithmic Lipschitz constant on bounded treewidth graphs. On such graphs, our result outperforms most existing Lipschitz continuous algorithms in terms of approximability and/or Lipschitz continuity. Further, we provide similar results for problems on bounded-clique-width graphs subject to constraints expressed in MSO₁. Additionally, we construct a Lipschitz continuous version of Baker’s decomposition using our meta-theorem as a subroutine.
Cite as

Tatsuya Gima, Soh Kumabe, and Yuichi Yoshida. Courcelle’s Theorem for Lipschitz Continuity. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gima_et_al:LIPIcs.ESA.2025.11,
  author =	{Gima, Tatsuya and Kumabe, Soh and Yoshida, Yuichi},
  title =	{{Courcelle’s Theorem for Lipschitz Continuity}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{11:1--11:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.11},
  URN =		{urn:nbn:de:0030-drops-244793},
  doi =		{10.4230/LIPIcs.ESA.2025.11},
  annote =	{Keywords: Fixed-Parameter Tractability, Algorithmic Meta-Theorem, Lipschitz Continuity}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.19
On the Enumeration of Signatures of XOR-CNF’s

Authors: Nadia Creignou, Oscar Defrain, Frédéric Olive, and Simon Vilmin

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
Given a CNF formula φ with clauses C_1, … , C_m over a set of variables V, a truth assignment 𝐚: V → {0, 1} generates a binary sequence σ_φ(𝐚) = (C_1(𝐚), …, C_m(𝐚)), called a signature of φ, where C_i(𝐚) = 1 if clause C_i evaluates to 1 under assignment 𝐚, and C_i(𝐚) = 0 otherwise. Signatures and their associated generation problems have given rise to new yet promising research questions in algorithmic enumeration. In a recent paper, Bérczi et al. interestingly proved that generating signatures of a CNF is tractable despite the fact that verifying a solution is hard. They also showed the hardness of finding maximal signatures of an arbitrary CNF due to the intractability of satisfiability in general. Their contribution leaves open the problem of efficiently generating maximal signatures for tractable classes of CNFs, i.e., those for which satisfiability can be solved in polynomial time. Stepping into that direction, we completely characterize the complexity of generating all, minimal, and maximal signatures for XOR-CNF’s.
Cite as

Nadia Creignou, Oscar Defrain, Frédéric Olive, and Simon Vilmin. On the Enumeration of Signatures of XOR-CNF’s. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 19:1-19:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{creignou_et_al:LIPIcs.WADS.2025.19,
  author =	{Creignou, Nadia and Defrain, Oscar and Olive, Fr\'{e}d\'{e}ric and Vilmin, Simon},
  title =	{{On the Enumeration of Signatures of XOR-CNF’s}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{19:1--19:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.19},
  URN =		{urn:nbn:de:0030-drops-242508},
  doi =		{10.4230/LIPIcs.WADS.2025.19},
  annote =	{Keywords: Algorithmic enumeration, XOR-CNF, signatures, maximal bipartite subgraphs enumeration, extension, proximity search}
}
Document
Research
DOI: 10.4230/OASIcs.Grossi.19
Designing Output Sensitive Algorithms for Subgraph Enumeration

Authors: Alessio Conte, Kazuhiro Kurita, Andrea Marino, Giulia Punzi, Takeaki Uno, and Kunihiro Wasa

Published in: OASIcs, Volume 132, From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday (2025)

Abstract
The enumeration of all subgraphs respecting some structural property is a fundamental task in theoretical computer science, with practical applications in many branches of data mining and network analysis. It is often of interest to only consider solutions (subgraphs) that are maximal under inclusion, and to achieve output-sensitive complexity, i.e., bounding the running time with respect to the number of subgraphs produced. In this paper, we provide a survey of techniques for designing output-sensitive algorithms for subgraph enumeration, including partition-based approaches such as flashlight search, solution-graph traversal methods such as reverse search, and cost amortization strategies such as push-out amortization. We also briefly discuss classes of efficiency, hardness of enumeration, and variants such as approximate enumeration. The paper is meant as an accessible handbook for learning the basics of the field and as a practical reference for selecting state-of-the-art subgraph enumeration strategies fitting to one’s needs.
Cite as

Alessio Conte, Kazuhiro Kurita, Andrea Marino, Giulia Punzi, Takeaki Uno, and Kunihiro Wasa. Designing Output Sensitive Algorithms for Subgraph Enumeration. In From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 132, pp. 19:1-19:40, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{conte_et_al:OASIcs.Grossi.19,
  author =	{Conte, Alessio and Kurita, Kazuhiro and Marino, Andrea and Punzi, Giulia and Uno, Takeaki and Wasa, Kunihiro},
  title =	{{Designing Output Sensitive Algorithms for Subgraph Enumeration}},
  booktitle =	{From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday},
  pages =	{19:1--19:40},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-391-1},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{132},
  editor =	{Conte, Alessio and Marino, Andrea and Rosone, Giovanna and Vitter, Jeffrey Scott},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Grossi.19},
  URN =		{urn:nbn:de:0030-drops-238180},
  doi =		{10.4230/OASIcs.Grossi.19},
  annote =	{Keywords: Graph algorithms, Graph enumeration, Output sensitive enumeration}
}
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.2025.19
Analyzing Self-Stabilization of Synchronous Unison via Propositional Satisfiability

Authors: Asma Khoualdia, Sami Cherif, Stéphane Devismes, and Léo Robert

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

Abstract
Synchronous unison is a classical clock synchronization problem in distributed computing, and especially in self-stabilization. This paper explores the self-stabilization of a synchronous unison algorithm proposed by Arora et al. using a propositional satisfiability-based approach. We give a logical formulation of the algorithm. This formulation includes the uniqueness of clock values at each node, the updates of clocks based on the minimum clock value in the neighborhood, and the detection of convergence or divergence. To optimize the models, additional constraints are introduced to reduce redundant cases of initial configurations to be analyzed. Our approach not only verifies the algorithm’s behaviour but also offers insights into enhancing its robustness and applicability to broader distributed systems.
Cite as

Asma Khoualdia, Sami Cherif, Stéphane Devismes, and Léo Robert. Analyzing Self-Stabilization of Synchronous Unison via Propositional Satisfiability. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 19:1-19:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{khoualdia_et_al:LIPIcs.CP.2025.19,
  author =	{Khoualdia, Asma and Cherif, Sami and Devismes, St\'{e}phane and Robert, L\'{e}o},
  title =	{{Analyzing Self-Stabilization of Synchronous Unison via Propositional Satisfiability}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{19:1--19:21},
  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.2025.19},
  URN =		{urn:nbn:de:0030-drops-238806},
  doi =		{10.4230/LIPIcs.CP.2025.19},
  annote =	{Keywords: Self-stabilization, Synchronous Unison, Satisfiability}
}
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.SAT.2025.23
Symbolic Conflict Analysis in Pseudo-Boolean Optimization

Authors: Robert Nieuwenhuis, Albert Oliveras, Enric Rodríguez-Carbonell, and Rui Zhao

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

Abstract
In the the last two decades, a lot of effort has been devoted to the development of satisfiability-checking tools for a variety of SAT-related problems. However, most of these tools lack optimization capabilities. That is, instead of finding any solution, one is sometimes interested in a solution that is best according to some criterion. Pseudo-Boolean solvers can be used to deal with optimization by successively solving a series of problems that contain an additional pseudo-Boolean constraint expressing that a better solution is required. A key point for the success of this simple approach is that lemmas that are learned for one problem can be reused for subsequent ones. In this paper we go one step further and show how, by using a simple symbolic conflict analysis procedure, not only can lemmas be reused between problems but also strengthened, thus further pruning the search space traversal. In addition, we show how this technique automatically allows one to infer upper bounds in maximization problems, thus giving an estimation of how far the solver is from finding an optimal solution. Experimental results with our PB solver reveal that (i) this technique is indeed effective in practice, providing important speedups in problems where several solutions are found and (ii) on problems with very few solutions, where the impact of our technique is limited, its overhead is negligible.
Cite as

Robert Nieuwenhuis, Albert Oliveras, Enric Rodríguez-Carbonell, and Rui Zhao. Symbolic Conflict Analysis in Pseudo-Boolean Optimization. In 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 341, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{nieuwenhuis_et_al:LIPIcs.SAT.2025.23,
  author =	{Nieuwenhuis, Robert and Oliveras, Albert and Rodr{\'\i}guez-Carbonell, Enric and Zhao, Rui},
  title =	{{Symbolic Conflict Analysis in Pseudo-Boolean Optimization}},
  booktitle =	{28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)},
  pages =	{23:1--23:18},
  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.2025.23},
  URN =		{urn:nbn:de:0030-drops-237579},
  doi =		{10.4230/LIPIcs.SAT.2025.23},
  annote =	{Keywords: SAT, Pseudo-Boolean Optimization, Conflict Analysis}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.78
The Role of Regularity in (Hyper-)Clique Detection and Implications for Optimizing Boolean CSPs

Authors: Nick Fischer, Marvin Künnemann, Mirza Redžić, and Julian Stieß

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

Abstract
Is detecting a k-clique in k-partite regular (hyper-)graphs as hard as in the general case? Intuition suggests yes, but proving this - especially for hypergraphs - poses notable challenges. Concretely, we consider a strong notion of regularity in h-uniform hypergraphs, where we essentially require that any subset of at most h-1 is incident to a uniform number of hyperedges. Such notions are studied intensively in the combinatorial block design literature. We show that any f(k)n^{g(k)}-time algorithm for detecting k-cliques in such graphs transfers to an f'(k)n^{g(k)}-time algorithm for the general case, establishing a fine-grained equivalence between the h-uniform hyperclique hypothesis and its natural regular analogue. Equipped with this regularization result, we then fully resolve the fine-grained complexity of optimizing Boolean constraint satisfaction problems over assignments with k non-zeros. Our characterization depends on the maximum degree d of a constraint function. Specifically, if d ≤ 1, we obtain a linear-time solvable problem, if d = 2, the time complexity is essentially equivalent to k-clique detection, and if d ≥ 3 the problem requires exhaustive-search time under the 3-uniform hyperclique hypothesis. To obtain our hardness results, the regularization result plays a crucial role, enabling a very convenient approach when applied carefully. We believe that our regularization result will find further applications in the future.
Cite as

Nick Fischer, Marvin Künnemann, Mirza Redžić, and Julian Stieß. The Role of Regularity in (Hyper-)Clique Detection and Implications for Optimizing Boolean CSPs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 78:1-78:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fischer_et_al:LIPIcs.ICALP.2025.78,
  author =	{Fischer, Nick and K\"{u}nnemann, Marvin and Red\v{z}i\'{c}, Mirza and Stie{\ss}, Julian},
  title =	{{The Role of Regularity in (Hyper-)Clique Detection and Implications for Optimizing Boolean CSPs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{78:1--78:18},
  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.2025.78},
  URN =		{urn:nbn:de:0030-drops-234559},
  doi =		{10.4230/LIPIcs.ICALP.2025.78},
  annote =	{Keywords: fine-grained complexity theory, clique detections in hypergraphs, constraint satisfaction, parameterized algorithms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.7
Parameterised Holant Problems

Authors: Panagiotis Aivasiliotis, Andreas Göbel, Marc Roth, and Johannes Schmitt

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

Abstract
We investigate the complexity of parameterised holant problems p-Holant(𝒮) for families of symmetric signatures 𝒮. The parameterised holant framework has been introduced by Curticapean in 2015 as a counter-part to the classical and well-established theory of holographic reductions and algorithms, and it constitutes an extensive family of coloured and weighted counting constraint satisfaction problems on graph-like structures, encoding as special cases various well-studied counting problems in parameterised and fine-grained complexity theory such as counting edge-colourful k-matchings, graph-factors, Eulerian orientations or, more generally, subgraphs with weighted degree constraints. We establish an exhaustive complexity trichotomy along the set of signatures 𝒮: Depending on the signatures, p-Holant(𝒮) is either 1) solvable in "FPT-near-linear time", i.e., in time f(k)⋅ 𝒪̃(|x|), or 2) solvable in "FPT-matrix-multiplication time", i.e., in time f(k)⋅ {𝒪}(n^{ω}), where n is the number of vertices of the underlying graph, but not solvable in FPT-near-linear time, unless the Triangle Conjecture fails, or 3) #W[1]-complete and no significant improvement over the naive brute force algorithm is possible unless the Exponential Time Hypothesis fails. This classification reveals a significant and surprising gap in the complexity landscape of parameterised Holants: Not only is every instance either fixed-parameter tractable or #W[1]-complete, but additionally, every FPT instance is solvable in time (at most) f(k)⋅ {𝒪}(n^{ω}). We show that there are infinitely many instances of each of the types; for example, all constant signatures yield holant problems of type (1), and the problem of counting edge-colourful k-matchings modulo p is of type (p) for p ∈ {2,3}. Finally, we also establish a complete classification for a natural uncoloured version of parameterised holant problem p-UnColHolant(𝒮), which encodes as special cases the non-coloured analogues of the aforementioned examples. We show that the complexity of p-UnColHolant(𝒮) is different: Depending on 𝒮 all instances are either solvable in FPT-near-linear time, or #W[1]-complete, that is, there are no instances of type (2).
Cite as

Panagiotis Aivasiliotis, Andreas Göbel, Marc Roth, and Johannes Schmitt. Parameterised Holant Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 7:1-7:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{aivasiliotis_et_al:LIPIcs.ICALP.2025.7,
  author =	{Aivasiliotis, Panagiotis and G\"{o}bel, Andreas and Roth, Marc and Schmitt, Johannes},
  title =	{{Parameterised Holant Problems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{7:1--7:14},
  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.2025.7},
  URN =		{urn:nbn:de:0030-drops-233842},
  doi =		{10.4230/LIPIcs.ICALP.2025.7},
  annote =	{Keywords: holant problems, counting problems, parameterised algorithms, fine-grained complexity theory, homomorphisms}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.148
Holant* Dichotomy on Domain Size 3: A Geometric Perspective

Authors: Jin-Yi Cai and Jin Soo Ihm

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

Abstract
Holant problems are a general framework to study the computational complexity of counting problems. It is a more expressive framework than counting constraint satisfaction problems (CSP) which are in turn more expressive than counting graph homomorphisms (GH). In this paper, we prove the first complexity dichotomy of Holant^*₃(ℱ) where ℱ is an arbitrary set of symmetric, real valued constraint functions on domain size 3. We give an explicit tractability criterion and prove that, if ℱ satisfies this criterion then Holant^*₃(ℱ) is polynomial time computable, and otherwise it is #P-hard, with no intermediate cases. We show that the geometry of the tensor decomposition of the constraint functions plays a central role in the formulation as well as the structural internal logic of the dichotomy.
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Jin-Yi Cai and Jin Soo Ihm. Holant* Dichotomy on Domain Size 3: A Geometric Perspective. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 148:1-148:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cai_et_al:LIPIcs.ICALP.2025.148,
  author =	{Cai, Jin-Yi and Ihm, Jin Soo},
  title =	{{Holant* Dichotomy on Domain Size 3: A Geometric Perspective}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{148:1--148:18},
  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.2025.148},
  URN =		{urn:nbn:de:0030-drops-235254},
  doi =		{10.4230/LIPIcs.ICALP.2025.148},
  annote =	{Keywords: Holant problem, Complexity dichotomy, Higher domain}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.86
Eulerian Orientations and Hadamard Codes: A Novel Connection via Counting

Authors: Shuai Shao and Zhuxiao Tang

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
We discover a novel connection between two classical mathematical notions, Eulerian orientations and Hadamard codes by studying the counting problem of Eulerian orientations (#EO) with local constraint functions imposed on vertices. We present two special classes of constraint functions and a chain reaction algorithm, and show that the #EO problem defined by each class alone is polynomial-time solvable by the algorithm. These tractable classes of functions are defined inductively, and quite remarkably the base level of these classes is characterized perfectly by the well-known Hadamard code. Thus, we establish a novel connection between counting Eulerian orientations and coding theory. We also prove a #P-hardness result for the #EO problem when constraint functions from the two tractable classes appear together.
Cite as

Shuai Shao and Zhuxiao Tang. Eulerian Orientations and Hadamard Codes: A Novel Connection via Counting. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 86:1-86:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{shao_et_al:LIPIcs.ITCS.2025.86,
  author =	{Shao, Shuai and Tang, Zhuxiao},
  title =	{{Eulerian Orientations and Hadamard Codes: A Novel Connection via Counting}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{86:1--86:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.86},
  URN =		{urn:nbn:de:0030-drops-227146},
  doi =		{10.4230/LIPIcs.ITCS.2025.86},
  annote =	{Keywords: Eulerian orientations, Hadamard codes, Counting problems, Tractable classes}
}
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