17 Search Results for "Jeavons, Peter"

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.STACS.2026.59
When Is Local Search Both Effective and Efficient?

Authors: Artem Kaznatcheev and Sofia Vazquez Alferez

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

Abstract
Combinatorial optimization problems implicitly define fitness landscapes that combine the numeric structure of the "fitness" function to be maximized with the combinatorial structure of which assignments are "adjacent". Local search starts at an assignment in this landscape and successively moves assignments until no further improvement is possible among the adjacent assignments. Classic analyses of local search algorithms have focused more on the question of effectiveness ("did we find a good solution?") and often implicitly assumed that there are no doubts about their efficiency ("did we find it quickly?"). But there are many reasons to doubt the efficiency of local search. Even if we focus on fitness landscapes on the hypercube that are single peaked on every subcube (known as semismooth fitness landscapes, completely unimodal pseudo-Boolean functions, or acyclic unique sink orientations) where effectiveness is obvious, many local search algorithms are known to be inefficient. Since fitness landscapes are unwieldy exponentially large objects, we focus on their polynomial-sized representations by instances of valued constraint satisfaction problems (VCSP). We define a "direction" for valued constraints such that directed VCSPs generate semismooth fitness landscapes. We call directed VCSPs oriented if they do not have any pair of variables with arcs in both directions. Since recognizing if a VCSP-instance is directed or oriented is coNP-complete, we generalized oriented VCSPs as conditionally-smooth fitness landscapes where the structural property of "conditionally-smooth" is recognizable in polynomial time for a VCSP-instance. We prove that many popular local search algorithms like random ascent, simulated annealing, history-based rules, jumping rules, and the Kernighan-Lin heuristic are very efficient on conditionally-smooth landscapes. But conditionally-smooth landscapes are still expressive enough so that other well-regarded local search algorithms like steepest ascent and random facet require a super-polynomial number of steps to find the fitness peak.
Cite as

Artem Kaznatcheev and Sofia Vazquez Alferez. When Is Local Search Both Effective and Efficient?. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 59:1-59:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kaznatcheev_et_al:LIPIcs.STACS.2026.59,
  author =	{Kaznatcheev, Artem and Vazquez Alferez, Sofia},
  title =	{{When Is Local Search Both Effective and Efficient?}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{59:1--59:19},
  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.2026.59},
  URN =		{urn:nbn:de:0030-drops-255480},
  doi =		{10.4230/LIPIcs.STACS.2026.59},
  annote =	{Keywords: valued constraint satisfaction problem, local search, algorithm analysis, constraint graphs, pseudo-Boolean functions, parameterized complexity}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.15
The Complexity of Resilience for Digraph Queries

Authors: Manuel Bodirsky and Žaneta Semanišinová

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

Abstract
We prove a complexity dichotomy for the resilience problem for unions of conjunctive digraph queries (i.e., for existential positive sentences over the signature {R} of directed graphs). Specifically, for every union μ of conjunctive digraph queries, the following problem is in P or NP-complete: given a directed multigraph G and a natural number u, can we remove u edges from G so that G ⊧ ¬ μ? In fact, we verify a more general dichotomy conjecture from [Bodirsky et al., 2024] for all resilience problems in the special case of directed graphs, and show that for such unions of queries μ there exists a countably infinite (`dual') valued structure Δ_μ which either primitively positively constructs 1-in-3-3-SAT, and hence the resilience problem for μ is NP-complete by general principles, or has a pseudo cyclic canonical fractional polymorphism, and the resilience problem for μ is in P.
Cite as

Manuel Bodirsky and Žaneta Semanišinová. The Complexity of Resilience for Digraph Queries. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 15:1-15:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bodirsky_et_al:LIPIcs.STACS.2026.15,
  author =	{Bodirsky, Manuel and Semani\v{s}inov\'{a}, \v{Z}aneta},
  title =	{{The Complexity of Resilience for Digraph Queries}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{15:1--15:20},
  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.2026.15},
  URN =		{urn:nbn:de:0030-drops-255045},
  doi =		{10.4230/LIPIcs.STACS.2026.15},
  annote =	{Keywords: valued constraints, unions of conjunctive queries, resilience, computational complexity, pp-constructions}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.14
Energy-Efficient Maximal Independent Sets in Radio Networks

Authors: Dominick Banasik, Varsha Dani, Fabien Dufoulon, Aayush Gupta, Thomas P. Hayes, and Gopal Pandurangan

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
The maximal independent set (MIS) is one of the most fundamental problems in distributed computing, and it has been studied intensively for over four decades. This paper focuses on the MIS problem in the radio network model, a standard model widely used to model wireless networks, particularly ad hoc wireless and sensor networks. Energy is a premium resource in these networks, which are typically battery-powered. Hence, designing distributed algorithms that use as little energy as possible is crucial. We use the well-established energy model where a node can be sleeping or awake in a round, and only the awake rounds (when it can send or listen) determine the energy complexity of the algorithm, which we want to minimize. We present new, more energy-efficient MIS algorithms in radio networks with arbitrary and unknown graph topology. We present algorithms for two popular variants of the radio model - with collision detection (CD) and without collision detection (no-CD). Specifically, we obtain the following results: 1) CD model: We present a randomized distributed MIS algorithm with energy complexity O(log n), round complexity O(log² n), and failure probability 1 / poly(n), where n is the network size. We show that our energy complexity is optimal by showing a matching Ω(log n) lower bound. 2) no-CD model: In the more challenging no-CD model, we present a randomized distributed MIS algorithm with energy complexity O(log²n log log n), round complexity O(log³ n log Δ), and failure probability 1 / poly(n). The energy complexity of our algorithm is significantly lower than the round (and energy) complexity of O(log³ n) of the best known distributed MIS algorithm of Davies [PODC 2023] for arbitrary graph topology.
Cite as

Dominick Banasik, Varsha Dani, Fabien Dufoulon, Aayush Gupta, Thomas P. Hayes, and Gopal Pandurangan. Energy-Efficient Maximal Independent Sets in Radio Networks. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 14:1-14:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{banasik_et_al:LIPIcs.DISC.2025.14,
  author =	{Banasik, Dominick and Dani, Varsha and Dufoulon, Fabien and Gupta, Aayush and Hayes, Thomas P. and Pandurangan, Gopal},
  title =	{{Energy-Efficient Maximal Independent Sets in Radio Networks}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{14:1--14:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.14},
  URN =		{urn:nbn:de:0030-drops-248311},
  doi =		{10.4230/LIPIcs.DISC.2025.14},
  annote =	{Keywords: Distributed Computing, Energy Complexity, Sleeping Model, Radio Networks, Maximal Independent Set}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.20
Beeping Deterministic CONGEST Algorithms in Graphs

Authors: Pawel Garncarek, Dariusz R. Kowalski, Shay Kutten, and Miguel A. Mosteiro

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

Abstract
Beeping Network (BN) is a popular graph-based model of wireless computation, which applies the OR operation to one-bit messages sent simultaneously by neighbors. It admits fast (polylogarithmic in the number of nodes n) randomized solutions to many graph problems, but all known deterministic algorithms for non-trivial graph problems are at least polynomial in the maximum node degree Δ. We improve known results for deterministic algorithms by showing that this polynomial can be as low as Õ(Δ²). More precisely, we show how to simulate a single round of any CONGEST algorithm in any network in O(Δ² polylog n) beeping rounds, each accommodating at most one beep per node, even if the nodes intend to send different messages to different neighbors. This upper bound reduces polynomially the time for a deterministic simulation of CONGEST in a Beeping Network, comparing to the best known algorithms, and nearly matches the time obtained recently using randomization (up to a poly-logarithmic factor) as well as the lower bound. Specifically, any algorithm designed for the CONGEST networks can be run in BNs with O(Δ² polylog n) multiplicative overhead, e.g., we can now deterministically compute an MIS in any BN in O(Δ² polylog n) beeping rounds, improving the previous best Θ(Δ³)-round solution. For h-hop simulations, we prove a lower bound Ω(Δ^{h+1}), and we design a nearly matching algorithm that is able to "pipeline" the node-to-node information in a faster way than beeping layer-by-layer.
Cite as

Pawel Garncarek, Dariusz R. Kowalski, Shay Kutten, and Miguel A. Mosteiro. Beeping Deterministic CONGEST Algorithms in Graphs. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 20:1-20:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{garncarek_et_al:LIPIcs.ESA.2025.20,
  author =	{Garncarek, Pawel and Kowalski, Dariusz R. and Kutten, Shay and Mosteiro, Miguel A.},
  title =	{{Beeping Deterministic CONGEST Algorithms in Graphs}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{20:1--20:17},
  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.2025.20},
  URN =		{urn:nbn:de:0030-drops-244880},
  doi =		{10.4230/LIPIcs.ESA.2025.20},
  annote =	{Keywords: Beeping Networks, CONGEST Networks, deterministic simulations, graph algorithms}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.19
On the Constant-Factor Approximability of Minimum Cost Constraint Satisfaction Problems

Authors: Ian DeHaan, Neng Huang, and Euiwoong Lee

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We study minimum cost constraint satisfaction problems (MinCostCSP) through the algebraic lens. We show that for any constraint language Γ which has the dual discriminator operation as a polymorphism, there exists a |D|-approximation algorithm for MinCostCSP(Γ) where D is the domain. Complementing our algorithmic result, we show that any constraint language Γ where MinCostCSP(Γ) admits a constant-factor approximation must have a near-unanimity (NU) polymorphism unless P = NP, extending a similar result by Dalmau et al. on MinCSPs. These results imply a dichotomy of constant-factor approximability for constraint languages that contain all permutation relations (a natural generalization for Boolean CSPs that allow variable negation): either MinCostCSP(Γ) has an NU polymorphism and is |D|-approximable, or it does not have any NU polymorphism and is NP-hard to approximate within any constant factor. Finally, we present a constraint language which has a majority polymorphism, but is nonetheless NP-hard to approximate within any constant factor assuming the Unique Games Conjecture, showing that the condition of having an NU polymorphism is in general not sufficient unless UGC fails.
Cite as

Ian DeHaan, Neng Huang, and Euiwoong Lee. On the Constant-Factor Approximability of Minimum Cost Constraint Satisfaction Problems. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 19:1-19:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dehaan_et_al:LIPIcs.APPROX/RANDOM.2025.19,
  author =	{DeHaan, Ian and Huang, Neng and Lee, Euiwoong},
  title =	{{On the Constant-Factor Approximability of Minimum Cost Constraint Satisfaction Problems}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{19:1--19:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.19},
  URN =		{urn:nbn:de:0030-drops-243851},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.19},
  annote =	{Keywords: Constraint satisfaction problems, approximation algorithms, polymorphisms}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.83
Three Fundamental Questions in Modern Infinite-Domain Constraint Satisfaction

Authors: Michael Pinsker, Jakub Rydval, Moritz Schöbi, and Christoph Spiess

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

Abstract
The Feder-Vardi dichotomy conjecture for Constraint Satisfaction Problems (CSPs) with finite templates, confirmed independently by Bulatov and Zhuk, has an extension to certain well-behaved infinite templates due to Bodirsky and Pinsker which remains wide open. We provide answers to three fundamental questions on the scope of the Bodirsky-Pinsker conjecture. Our first two main results provide two simplifications of this scope, one of structural, and the other one of algebraic nature. The former simplification implies that the conjecture is equivalent to its restriction to templates without algebraicity, a crucial assumption in the most powerful classification methods. The latter yields that the higher-arity invariants of any template within its scope can be assumed to be essentially injective, and any algebraic condition characterizing any complexity class within the conjecture closed under Datalog reductions must be satisfiable by injections, thus lifting the mystery of the better applicability of certain conditions over others. Our third main result uses the first one to show that any non-trivially tractable template within the scope serves, up to a Datalog-computable modification of it, as the witness of the tractability of a non-finitely tractable finite-domain Promise Constraint Satisfaction Problem (PCSP) by the so-called sandwich method. This generalizes a recent result of Mottet and provides a strong hitherto unknown connection between the Bodirsky-Pinsker conjecture and finite-domain PCSPs.
Cite as

Michael Pinsker, Jakub Rydval, Moritz Schöbi, and Christoph Spiess. Three Fundamental Questions in Modern Infinite-Domain Constraint Satisfaction. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 83:1-83:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{pinsker_et_al:LIPIcs.MFCS.2025.83,
  author =	{Pinsker, Michael and Rydval, Jakub and Sch\"{o}bi, Moritz and Spiess, Christoph},
  title =	{{Three Fundamental Questions in Modern Infinite-Domain Constraint Satisfaction}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{83:1--83:20},
  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.2025.83},
  URN =		{urn:nbn:de:0030-drops-241903},
  doi =		{10.4230/LIPIcs.MFCS.2025.83},
  annote =	{Keywords: (Promise) Constraint Satisfaction Problem, dichotomy conjecture, polymorphism, identity, algebraicity, homogeneity, \omega-categoricity, finite boundedness, Datalog}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.24
Temporal Valued Constraint Satisfaction Problems

Authors: Manuel Bodirsky, Édouard Bonnet, and Žaneta Semanišinová

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

Abstract
We study the computational complexity of the valued constraint satisfaction problem (VCSP) for every valued structure over ℚ that is preserved by all order-preserving bijections. Such VCSPs will be called temporal, in analogy to the (classical) constraint satisfaction problem: a relational structure is preserved by all order-preserving bijections if and only if all its relations have a first-order definition in (ℚ; <), and the CSPs for such structures are called temporal CSPs. Many optimization problems that have been studied intensively in the literature can be phrased as a temporal VCSP. We prove that a temporal VCSP is in P, or NP-complete. Our analysis uses the concept of fractional polymorphisms. This is the first dichotomy result for VCSPs over infinite domains which is complete in the sense that it treats all valued structures that contain a given automorphism group.
Cite as

Manuel Bodirsky, Édouard Bonnet, and Žaneta Semanišinová. Temporal Valued Constraint Satisfaction Problems. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bodirsky_et_al:LIPIcs.MFCS.2025.24,
  author =	{Bodirsky, Manuel and Bonnet, \'{E}douard and Semani\v{s}inov\'{a}, \v{Z}aneta},
  title =	{{Temporal Valued Constraint Satisfaction Problems}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{24:1--24:19},
  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.2025.24},
  URN =		{urn:nbn:de:0030-drops-241311},
  doi =		{10.4230/LIPIcs.MFCS.2025.24},
  annote =	{Keywords: Constraint Satisfaction Problems, valued CSPs, temporal CSPs, fractional polymorphisms, complexity dichotomy, min CSPs}
}
Document
DOI: 10.4230/LIPIcs.CP.2025.18
Greed Is Slow on Sparse Graphs of Oriented Valued Constraints

Authors: Artem Kaznatcheev and Sofia Vazquez Alferez

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

Abstract
Greedy local search is especially popular for solving valued constraint satisfaction problems (VCSPs). Since any method will be slow for some VCSPs, we ask: what is the simplest VCSP on which greedy local search is slow? We construct a VCSP on 6n Boolean variables for which greedy local search takes 7(2ⁿ - 1) steps to find the unique peak. Our VCSP is simple in two ways. First, it is very sparse: its constraint graph has pathwidth 2 and maximum degree 3. This is the simplest VCSP on which some local search could be slow. Second, it is "oriented" – there is an ordering on the variables such that later variables are conditionally-independent of earlier ones. Being oriented allows many non-greedy local search methods to find the unique peak in a quadratic number of steps. Thus, we conclude that - among local search methods - greed is particularly slow.
Cite as

Artem Kaznatcheev and Sofia Vazquez Alferez. Greed Is Slow on Sparse Graphs of Oriented Valued Constraints. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 18:1-18:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kaznatcheev_et_al:LIPIcs.CP.2025.18,
  author =	{Kaznatcheev, Artem and Vazquez Alferez, Sofia},
  title =	{{Greed Is Slow on Sparse Graphs of Oriented Valued Constraints}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{18:1--18:13},
  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.2025.18},
  URN =		{urn:nbn:de:0030-drops-238793},
  doi =		{10.4230/LIPIcs.CP.2025.18},
  annote =	{Keywords: valued constraint satisfaction problem, local search, algorithm analysis, constraint graphs}
}
Document
DOI: 10.4230/LIPIcs.SAT.2025.29
Reencoding Unique Literal Clauses

Authors: Aeacus Sheng, Joseph E. Reeves, and Marijn J. H. Heule

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

Abstract
We present a lightweight reencoding technique that augments propositional formulas containing implicit or explicit exactly-one constraints with auxiliary variables derived from the order encoding. Our approach is based on the observation that many formulas contain clauses where each literal appears only in that clause, and that these unique literal clauses can be replaced by the corresponding sequential counter encoding of exactly-one constraints, which introduces the same variables as the order encoding. We implemented the reencoding in the state-of-the-art SAT solver CaDiCaL with support for proof logging and solution reconstruction. Experiments on SAT Competition benchmarks demonstrate that our technique enables solving dozens of additional formulas. We found that shuffling a formula before reencoding harms performance. To mitigate this issue, we introduce a method that sorts literals within clauses based on the formula structure before applying our reencoding. The same technique also predicts whether reencoding is likely to yield improvements.
Cite as

Aeacus Sheng, Joseph E. Reeves, and Marijn J. H. Heule. Reencoding Unique Literal Clauses. In 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 341, pp. 29:1-29:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sheng_et_al:LIPIcs.SAT.2025.29,
  author =	{Sheng, Aeacus and Reeves, Joseph E. and Heule, Marijn J. H.},
  title =	{{Reencoding Unique Literal Clauses}},
  booktitle =	{28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)},
  pages =	{29:1--29:21},
  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.2025.29},
  URN =		{urn:nbn:de:0030-drops-237635},
  doi =		{10.4230/LIPIcs.SAT.2025.29},
  annote =	{Keywords: Satisfiability solving, auxiliary variables, graph coloring}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.34
On the Degree Automatability of Sum-Of-Squares Proofs

Authors: Alex Bortolotti, Monaldo Mastrolilli, and Luis Felipe Vargas

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

Abstract
The Sum-of-Squares (SoS) hierarchy, also known as Lasserre hierarchy, has emerged as a promising tool in optimization. However, it remains unclear whether fixed-degree SoS proofs can be automated [O'Donnell (2017)]. Indeed, there are examples of polynomial systems with bounded coefficients that admit low-degree SoS proofs, but these proofs necessarily involve numbers with an exponential number of bits, implying that low-degree SoS proofs cannot always be found efficiently. A sufficient condition derived from the Nullstellensatz proof system [Raghavendra and Weitz (2017)] identifies cases where bit complexity issues can be circumvented. One of the main problems left open by Raghavendra and Weitz is proving any result for refutations, as their condition applies only to polynomial systems with a large set of solutions. In this work, we broaden the class of polynomial systems for which degree-d SoS proofs can be automated. To achieve this, we develop a new criterion and we demonstrate how our criterion applies to polynomial systems beyond the scope of Raghavendra and Weitz’s result. In particular, we establish a separation for instances arising from Constraint Satisfaction Problems (CSPs). Moreover, our result extends to refutations, establishing that polynomial-time refutation is possible for broad classes of polynomial time solvable constraint problems, highlighting a first advancement in this area.
Cite as

Alex Bortolotti, Monaldo Mastrolilli, and Luis Felipe Vargas. On the Degree Automatability of Sum-Of-Squares Proofs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 34:1-34:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bortolotti_et_al:LIPIcs.ICALP.2025.34,
  author =	{Bortolotti, Alex and Mastrolilli, Monaldo and Vargas, Luis Felipe},
  title =	{{On the Degree Automatability of Sum-Of-Squares Proofs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{34:1--34:19},
  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.2025.34},
  URN =		{urn:nbn:de:0030-drops-234110},
  doi =		{10.4230/LIPIcs.ICALP.2025.34},
  annote =	{Keywords: Sum of squares, Polynomial calculus, Polynomial ideal membership, Polymorphisms, Gr\"{o}bner basis theory, Constraint satisfaction problems, Proof complexity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.37
Satisfiability of Commutative vs. Non-Commutative CSPs

Authors: Andrei A. Bulatov and Stanislav Živný

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

Abstract
The Mermin-Peres magic square is a celebrated example of a system of Boolean linear equations that is not (classically) satisfiable but is satisfiable via linear operators on a Hilbert space of dimension four. A natural question is then, for what kind of problems such a phenomenon occurs? Atserias, Kolaitis, and Severini answered this question for all Boolean Constraint Satisfaction Problems (CSPs): For 0-Valid-SAT, 1-Valid-SAT, 2-SAT, Horn-SAT, and Dual Horn-SAT, classical satisfiability and operator satisfiability is the same and thus there is no gap; for all other Boolean CSPs, these notions differ as there are gaps, i.e., there are unsatisfiable instances that are satisfiable via operators on Hilbert spaces. We generalize their result to CSPs on arbitrary finite domains and give an almost complete classification: First, we show that NP-hard CSPs admit a separation between classical satisfiability and satisfiability via operators on finite- and infinite-dimensional Hilbert spaces. Second, we show that tractable CSPs of bounded width have no satisfiability gaps of any kind. Finally, we show that tractable CSPs of unbounded width can simulate, in a satisfiability-gap-preserving fashion, linear equations over an Abelian group of prime order p; for such CSPs, we obtain a separation of classical satisfiability and satisfiability via operators on infinite-dimensional Hilbert spaces. Furthermore, if p = 2, such CSPs also have gaps separating classical satisfiability and satisfiability via operators on finite- and infinite-dimensional Hilbert spaces.
Cite as

Andrei A. Bulatov and Stanislav Živný. Satisfiability of Commutative vs. Non-Commutative CSPs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 37:1-37:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bulatov_et_al:LIPIcs.ICALP.2025.37,
  author =	{Bulatov, Andrei A. and \v{Z}ivn\'{y}, Stanislav},
  title =	{{Satisfiability of Commutative vs. Non-Commutative CSPs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{37:1--37:18},
  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.2025.37},
  URN =		{urn:nbn:de:0030-drops-234149},
  doi =		{10.4230/LIPIcs.ICALP.2025.37},
  annote =	{Keywords: constraint satisfaction, quantum CSP, operator CSP}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.60
Modular Counting CSP: Reductions and Algorithms

Authors: Amirhossein Kazeminia and Andrei A. Bulatov

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
The Constraint Satisfaction Problem (CSP) is ubiquitous in various areas of mathematics and computer science. Many of its variations have been studied including the Counting CSP, where the goal is to find the number of solutions to a CSP instance. The complexity of finding the exact number of solutions of a CSP is well understood (Bulatov, 2013, and Dyer and Richerby, 2013) and the focus has shifted to other variations of the Counting CSP such as counting the number of solutions modulo an integer. This problem has attracted considerable attention recently. In the case of CSPs based on undirected graphs Bulatov and Kazeminia (STOC 2022) obtained a complexity classification for the problem of counting solutions modulo p for arbitrary prime p. In this paper we report on the progress made towards a similar classification for the general CSP, not necessarily based on graphs. We identify several features that make the general case very different from the graph case such as a stronger form of rigidity and the structure of automorphisms of powers of relational structures. We provide a solution algorithm in the case p = 2 that works under some additional conditions and prove the hardness of the problem under some assumptions about automorphisms of the powers of the relational structure. We also reduce the general CSP to the case that only uses binary relations satisfying strong additional conditions.
Cite as

Amirhossein Kazeminia and Andrei A. Bulatov. Modular Counting CSP: Reductions and Algorithms. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 60:1-60:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kazeminia_et_al:LIPIcs.STACS.2025.60,
  author =	{Kazeminia, Amirhossein and Bulatov, Andrei A.},
  title =	{{Modular Counting CSP: Reductions and Algorithms}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{60:1--60:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine 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.2025.60},
  URN =		{urn:nbn:de:0030-drops-228853},
  doi =		{10.4230/LIPIcs.STACS.2025.60},
  annote =	{Keywords: Constraint Satisfaction Problem, Modular Counting}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2024.33
Self-Stabilizing Fully Adaptive Maximal Matching

Authors: Shimon Bitton, Yuval Emek, Taisuke Izumi, and Shay Kutten

Published in: LIPIcs, Volume 324, 28th International Conference on Principles of Distributed Systems (OPODIS 2024)

Abstract
A self-stabilizing randomized algorithm for mending maximal matching (MM) in synchronous networks is presented. Starting from a legal MM configuration and assuming that the network undergoes k faults or topology changes (that may occur in multiple batches), the algorithm is guaranteed to stabilize back to a legal MM configuration in time O(log k) in expectation and with high probability (in k), using constant size messages. The algorithm is simple to implement and is uniform in the sense that it does not assume unique identifiers, nor does it assume any global knowledge of the communication graph including its size. It relies on a generic probabilistic phase synchronization technique that may be useful for other self-stabilizing problems. The algorithm compares favorably with the existing self-stabilizing MM algorithms in terms of the dependence of its run-time on k, a.k.a. fully adaptive run-time. In fact, this dependence is asymptotically optimal for uniform algorithms that use constant size messages.
Cite as

Shimon Bitton, Yuval Emek, Taisuke Izumi, and Shay Kutten. Self-Stabilizing Fully Adaptive Maximal Matching. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 33:1-33:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bitton_et_al:LIPIcs.OPODIS.2024.33,
  author =	{Bitton, Shimon and Emek, Yuval and Izumi, Taisuke and Kutten, Shay},
  title =	{{Self-Stabilizing Fully Adaptive Maximal Matching}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{33:1--33:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.33},
  URN =		{urn:nbn:de:0030-drops-225698},
  doi =		{10.4230/LIPIcs.OPODIS.2024.33},
  annote =	{Keywords: self-stabilization, maximal matching, fully adaptive run-time, dynamic graphs}
}
Document
DOI: 10.4230/LIPIcs.CP.2024.17
Exponential Steepest Ascent from Valued Constraint Graphs of Pathwidth Four

Authors: Artem Kaznatcheev and Melle van Marle

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

Abstract
We examine the complexity of maximising fitness via local search on valued constraint satisfaction problems (VCSPs). We consider two kinds of local ascents: (1) steepest ascents, where each step changes the domain that produces a maximal increase in fitness; and (2) ≺-ordered ascents, where - of the domains with available fitness increasing changes - each step changes the ≺-minimal domain. We provide a general padding argument to simulate any ordered ascent by a steepest ascent. We construct a VCSP that is a path of binary constraints between alternating 2-state and 3-state domains with exponentially long ordered ascents. We apply our padding argument to this VCSP to obtain a Boolean VCSP that has a constraint (hyper)graph of arity 5 and pathwidth 4 with exponential steepest ascents. This is an improvement on the previous best known construction for long steepest ascents, which had arity 8 and pathwidth 7.
Cite as

Artem Kaznatcheev and Melle van Marle. Exponential Steepest Ascent from Valued Constraint Graphs of Pathwidth Four. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kaznatcheev_et_al:LIPIcs.CP.2024.17,
  author =	{Kaznatcheev, Artem and van Marle, Melle},
  title =	{{Exponential Steepest Ascent from Valued Constraint Graphs of Pathwidth Four}},
  booktitle =	{30th International Conference on Principles and Practice of Constraint Programming (CP 2024)},
  pages =	{17:1--17:16},
  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.2024.17},
  URN =		{urn:nbn:de:0030-drops-207021},
  doi =		{10.4230/LIPIcs.CP.2024.17},
  annote =	{Keywords: valued constraint satisfaction problem, steepest ascent, local search, bounded treewidth, intractability}
}
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