14 Search Results for "Kozik, Jakub"

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
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.166
Limitations of Affine Integer Relaxations for Solving Constraint Satisfaction Problems

Authors: Moritz Lichter and Benedikt Pago

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

Abstract
We show that various recent algorithms for finite-domain constraint satisfaction problems (CSP), which are based on solving their affine integer relaxations, do not solve all tractable and not even all Maltsev CSPs. This rules them out as candidates for a universal polynomial-time CSP algorithm. The algorithms are ℤ-affine k-consistency, BLP+AIP, BA^{k}, and CLAP. We thereby answer a question by Brakensiek, Guruswami, Wrochna, and Živný [Joshua Brakensiek et al., 2020] whether a constant level of BA^{k}solves all tractable CSPs in the negative: Indeed, not even a sublinear level k suffices. We also refute a conjecture by Dalmau and Opršal [Víctor Dalmau and Jakub Opršal, 2024] (LICS 2024) that every CSP is either solved by ℤ-affine k-consistency or admits a Datalog reduction from 3-colorability. For the cohomological k-consistency algorithm, that is also based on affine relaxations, we show that it correctly solves our counterexample but fails on an NP-complete template.
Cite as

Moritz Lichter and Benedikt Pago. Limitations of Affine Integer Relaxations for Solving Constraint Satisfaction Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 166:1-166:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lichter_et_al:LIPIcs.ICALP.2025.166,
  author =	{Lichter, Moritz and Pago, Benedikt},
  title =	{{Limitations of Affine Integer Relaxations for Solving Constraint Satisfaction Problems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{166:1--166:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.166},
  URN =		{urn:nbn:de:0030-drops-235431},
  doi =		{10.4230/LIPIcs.ICALP.2025.166},
  annote =	{Keywords: constraint satisfaction, affine relaxation, promise CSPs, \mathbb{Z}-affine k-consistency, cohomological k-consistency algorithm, Tseitin, graph isomorphism}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.158
Restricted CSPs and F-Free Digraph Algorithmics

Authors: Santiago Guzmán-Pro and Barnaby Martin

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

Abstract
In recent years, much attention has been placed on the complexity of graph homomorphism problems when the input is restricted to ℙ_k-free and ℙ_k-subgraph-free graphs. We consider the directed version of this research line, by addressing the question is it true that digraph homomorphism problems CSP(H) have a P versus NP-complete dichotomy when the input is restricted to ℙ→_k-free (resp. ℙ→_k-subgraph-free) digraphs? Our main contribution in this direction shows that if CSP(H) is NP-complete, then there is a positive integer N such that CSP(H) remains NP-hard even for ℙ→_N-subgraph-free digraphs. Moreover, CSP(H) becomes polynomial-time solvable for ℙ→_{N-1}-subgraph-free acyclic digraphs. We then verify the questions above for digraphs on three vertices and a family of smooth tournaments. We prove these results by establishing a connection between F-(subgraph)-free algorithmics and constraint satisfaction theory. On the way, we introduce restricted CSPs, i.e., problems of the form CSP(H) restricted to yes-instances of CSP(H') - these were called restricted homomorphism problems by Hell and Nešetřil. Another main result of this paper presents a P versus NP-complete dichotomy for these problems. Moreover, this complexity dichotomy is accompanied by an algebraic dichotomy in the spirit of the finite domain CSP dichotomy.
Cite as

Santiago Guzmán-Pro and Barnaby Martin. Restricted CSPs and F-Free Digraph Algorithmics. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 158:1-158:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{guzmanpro_et_al:LIPIcs.ICALP.2025.158,
  author =	{Guzm\'{a}n-Pro, Santiago and Martin, Barnaby},
  title =	{{Restricted CSPs and F-Free Digraph Algorithmics}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{158:1--158:21},
  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.2025.158},
  URN =		{urn:nbn:de:0030-drops-235352},
  doi =		{10.4230/LIPIcs.ICALP.2025.158},
  annote =	{Keywords: Digraph homomorphisms, constraint satisfaction problems, subgraph-free algorithmics}
}
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
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.143
Density of Rational Languages Under Shift Invariant Measures

Authors: Valérie Berthé, Herman Goulet-Ouellet, and Dominique Perrin

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

Abstract
We study density of rational languages under shift invariant probability measures on spaces of two-sided infinite words, which generalizes the classical notion of density studied in formal languages and automata theory. The density for a language is defined as the limit in average (if it exists) of the probability that a word of a given length belongs to the language. We establish the existence of densities for all rational languages under all shift invariant measures. We also give explicit formulas under certain conditions, in particular when the language is aperiodic. Our approach combines tools and ideas from semigroup theory and ergodic theory.
Cite as

Valérie Berthé, Herman Goulet-Ouellet, and Dominique Perrin. Density of Rational Languages Under Shift Invariant Measures. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 143:1-143:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{berthe_et_al:LIPIcs.ICALP.2025.143,
  author =	{Berth\'{e}, Val\'{e}rie and Goulet-Ouellet, Herman and Perrin, Dominique},
  title =	{{Density of Rational Languages Under Shift Invariant Measures}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{143:1--143:20},
  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.2025.143},
  URN =		{urn:nbn:de:0030-drops-235203},
  doi =		{10.4230/LIPIcs.ICALP.2025.143},
  annote =	{Keywords: Automata theory, Symbolic dynamics, Semigroup theory, Ergodic theory}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.169
Complexity of Approximate Conflict-Free, Linearly-Ordered, and Nonmonochromatic Hypergraph Colourings

Authors: Tamio-Vesa Nakajima, Zephyr Verwimp, Marcin Wrochna, and Stanislav Živný

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

Abstract
Using the algebraic approach to promise constraint satisfaction problems, we establish complexity classifications of three natural variants of hypergraph colourings: standard nonmonochromatic colourings, conflict-free colourings, and linearly-ordered colourings. Firstly, we show that finding an 𝓁-colouring of a k-colourable r-uniform hypergraph is NP-hard for all constant 2 ≤ k ≤ 𝓁 and r ≥ 3. This provides a shorter proof of a celebrated result by Dinur et al. [FOCS'02/Combinatorica'05]. Secondly, we show that finding an 𝓁-conflict-free colouring of an r-uniform hypergraph that admits a k-conflict-free colouring is NP-hard for all constant 2 ≤ k ≤ 𝓁 and r ≥ 4, except for r = 4 and k = 2 (and any 𝓁); this case is solvable in polynomial time. The case of r = 3 is the standard nonmonochromatic colouring, and the case of r = 2 is the notoriously difficult open problem of approximate graph colouring. Thirdly, we show that finding an 𝓁-linearly-ordered colouring of an r-uniform hypergraph that admits a k-linearly-ordered colouring is NP-hard for all constant 3 ≤ k ≤ 𝓁 and r ≥ 4, thus improving on the results of Nakajima and Živný [ICALP'22/ACM TocT'23].
Cite as

Tamio-Vesa Nakajima, Zephyr Verwimp, Marcin Wrochna, and Stanislav Živný. Complexity of Approximate Conflict-Free, Linearly-Ordered, and Nonmonochromatic Hypergraph Colourings. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 169:1-169:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{nakajima_et_al:LIPIcs.ICALP.2025.169,
  author =	{Nakajima, Tamio-Vesa and Verwimp, Zephyr and Wrochna, Marcin and \v{Z}ivn\'{y}, Stanislav},
  title =	{{Complexity of Approximate Conflict-Free, Linearly-Ordered, and Nonmonochromatic Hypergraph Colourings}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{169:1--169:10},
  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.2025.169},
  URN =		{urn:nbn:de:0030-drops-235460},
  doi =		{10.4230/LIPIcs.ICALP.2025.169},
  annote =	{Keywords: hypergraph colourings, conflict-free colourings, unique-maximum colourings, linearly-ordered colourings}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.24
An 11/6-Approximation Algorithm for Vertex Cover on String Graphs

Authors: Édouard Bonnet and Paweł Rzążewski

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
We present a 1.8334-approximation algorithm for Vertex Cover on string graphs given with a representation, which takes polynomial time in the size of the representation; the exact approximation factor is 11/6. Recently, the barrier of 2 was broken by Lokshtanov, Panolan, Saurabh, Xue, and Zehavi [SoGC '24] with a 1.9999-approximation algorithm. Thus we increase by three orders of magnitude the distance of the approximation ratio to the trivial bound of 2. Our algorithm is very simple. The intricacies reside in its analysis, where we mainly establish that string graphs without odd cycles of length at most 11 are 8-colorable. Previously, Chudnovsky, Scott, and Seymour [JCTB '21] showed that string graphs without odd cycles of length at most 7 are 80-colorable, and string graphs without odd cycles of length at most 5 have bounded chromatic number.
Cite as

Édouard Bonnet and Paweł Rzążewski. An 11/6-Approximation Algorithm for Vertex Cover on String Graphs. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 24:1-24:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bonnet_et_al:LIPIcs.SoCG.2025.24,
  author =	{Bonnet, \'{E}douard and Rz\k{a}\.{z}ewski, Pawe{\l}},
  title =	{{An 11/6-Approximation Algorithm for Vertex Cover on String Graphs}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{24:1--24:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.24},
  URN =		{urn:nbn:de:0030-drops-231764},
  doi =		{10.4230/LIPIcs.SoCG.2025.24},
  annote =	{Keywords: Approximation algorithms, string graphs, Vertex Cover, Coloring, odd girth}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2025.13
Symmetric Linear Arc Monadic Datalog and Gadget Reductions

Authors: Manuel Bodirsky and Florian Starke

Published in: LIPIcs, Volume 328, 28th International Conference on Database Theory (ICDT 2025)

Abstract
A Datalog program solves a constraint satisfaction problem (CSP) if and only if it derives the goal predicate precisely on the unsatisfiable instances of the CSP. There are three Datalog fragments that are particularly important for finite-domain constraint satisfaction: arc monadic Datalog, linear Datalog, and symmetric linear Datalog, each having good computational properties. We consider the fragment of Datalog where we impose all of these restrictions simultaneously, i.e., we study symmetric linear arc monadic (slam) Datalog. We characterise the CSPs that can be solved by a slam Datalog program as those that have a gadget reduction to a particular Boolean constraint satisfaction problem. We also present exact characterisations in terms of a homomorphism duality (which we call unfolded caterpillar duality), and in universal-algebraic terms (using known minor conditions, namely the existence of quasi Maltsev operations and k-absorptive operations of arity nk, for all n,k ≥ 1). Our characterisations also imply that the question whether a given finite-domain CSP can be expressed by a slam Datalog program is decidable.
Cite as

Manuel Bodirsky and Florian Starke. Symmetric Linear Arc Monadic Datalog and Gadget Reductions. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 13:1-13:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bodirsky_et_al:LIPIcs.ICDT.2025.13,
  author =	{Bodirsky, Manuel and Starke, Florian},
  title =	{{Symmetric Linear Arc Monadic Datalog and Gadget Reductions}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{13:1--13:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-364-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{328},
  editor =	{Roy, Sudeepa and Kara, Ahmet},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2025.13},
  URN =		{urn:nbn:de:0030-drops-229548},
  doi =		{10.4230/LIPIcs.ICDT.2025.13},
  annote =	{Keywords: Datalog, Gadget Reductions, Homomorphism Dualities, Minor Conditions}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.16
Undefinability of Approximation of 2-To-2 Games

Authors: Anuj Dawar and Bálint Molnár

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
Recent work by Atserias and Dawar [Albert Atserias and Anuj Dawar, 2019] and Tucker-Foltz [Jamie Tucker-Foltz, 2024] has established undefinability results in fixed-point logic with counting (FPC) corresponding to many classical complexity results from the hardness of approximation. In this line of work, NP-hardness results are turned into unconditional FPC undefinability results. We extend this work by showing the FPC undefinability of any constant factor approximation of weighted 2-to-2 games, based on the NP-hardness results of Khot, Minzer and Safra. Our result shows that the completely satisfiable 2-to-2 games are not FPC-separable from those that are not ε-satisfiable, for arbitrarily small ε. The perfect completeness of our inseparability is an improvement on the complexity result, as the NP-hardness of such a separation is still only conjectured. This perfect completeness enables us to show the FPC undefinability of other problems whose NP-hardness is conjectured. In particular, we are able to show that no FPC formula can separate the 3-colourable graphs from those that are not t-colourable, for any constant t.
Cite as

Anuj Dawar and Bálint Molnár. Undefinability of Approximation of 2-To-2 Games. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 16:1-16:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dawar_et_al:LIPIcs.CSL.2025.16,
  author =	{Dawar, Anuj and Moln\'{a}r, B\'{a}lint},
  title =	{{Undefinability of Approximation of 2-To-2 Games}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{16:1--16:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.16},
  URN =		{urn:nbn:de:0030-drops-227735},
  doi =		{10.4230/LIPIcs.CSL.2025.16},
  annote =	{Keywords: Hardness of Approximation, Unique Games, Descriptive Complexity, Fixed-Point Logic with Counting}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.48
Local Computation Algorithms for Hypergraph Coloring - Following Beck’s Approach

Authors: Andrzej Dorobisz and Jakub Kozik

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
We investigate local computation algorithms (LCA) for two-coloring of k-uniform hypergraphs. We focus on hypergraph instances that satisfy strengthened assumption of the Lovász Local Lemma of the form 2^(1-αk) (Δ+1) e < 1, where Δ is the bound on the maximum edge degree. The main question which arises here is for how large α there exists an LCA that is able to properly color such hypergraphs in polylogarithmic time per query. We describe briefly how upgrading the classical sequential procedure of Beck from 1991 with Moser and Tardos' Resample yields polylogarithmic LCA that works for α up to 1/4. Then, we present an improved procedure that solves wider range of instances by allowing α up to 1/3.
Cite as

Andrzej Dorobisz and Jakub Kozik. Local Computation Algorithms for Hypergraph Coloring - Following Beck’s Approach. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 48:1-48:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{dorobisz_et_al:LIPIcs.ICALP.2023.48,
  author =	{Dorobisz, Andrzej and Kozik, Jakub},
  title =	{{Local Computation Algorithms for Hypergraph Coloring - Following Beck’s Approach}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{48:1--48:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel 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.2023.48},
  URN =		{urn:nbn:de:0030-drops-181002},
  doi =		{10.4230/LIPIcs.ICALP.2023.48},
  annote =	{Keywords: Local Computation Algorithms, Hypergraph Coloring, Property B}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.89
Improving Gebauer’s Construction of 3-Chromatic Hypergraphs with Few Edges

Authors: Jakub Kozik

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
In 1964 Erdős proved, by randomized construction, that the minimum number of edges in a k-graph that is not two colorable is O(k² 2^k). To this day, it is not known whether there exist such k-graphs with smaller number of edges. Known deterministic constructions use much larger number of edges. The most recent one by Gebauer requires 2^{k+Θ(k^{2/3})} edges. Applying a derandomization technique we reduce that number to 2^{k+Θ̃(k^{1/2})}.
Cite as

Jakub Kozik. Improving Gebauer’s Construction of 3-Chromatic Hypergraphs with Few Edges. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 89:1-89:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{kozik:LIPIcs.ICALP.2021.89,
  author =	{Kozik, Jakub},
  title =	{{Improving Gebauer’s Construction of 3-Chromatic Hypergraphs with Few Edges}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{89:1--89:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.89},
  URN =		{urn:nbn:de:0030-drops-141587},
  doi =		{10.4230/LIPIcs.ICALP.2021.89},
  annote =	{Keywords: Property B, Hypergraph Coloring, Deterministic Constructions}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.46
A Note on Two-Colorability of Nonuniform Hypergraphs

Authors: Lech Duraj, Grzegorz Gutowski, and Jakub Kozik

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
For a hypergraph H, let q(H) denote the expected number of monochromatic edges when the color of each vertex in H is sampled uniformly at random from the set of size 2. Let s_{min}(H) denote the minimum size of an edge in H. Erdös asked in 1963 whether there exists an unbounded function g(k) such that any hypergraph H with s_{min}(H) >=slant k and q(H) <=slant g(k) is two colorable. Beck in 1978 answered this question in the affirmative for a function g(k) = Theta(log^* k). We improve this result by showing that, for an absolute constant delta>0, a version of random greedy coloring procedure is likely to find a proper two coloring for any hypergraph H with s_{min}(H) >=slant k and q(H) <=slant delta * log k.
Cite as

Lech Duraj, Grzegorz Gutowski, and Jakub Kozik. A Note on Two-Colorability of Nonuniform Hypergraphs. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 46:1-46:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{duraj_et_al:LIPIcs.ICALP.2018.46,
  author =	{Duraj, Lech and Gutowski, Grzegorz and Kozik, Jakub},
  title =	{{A Note on Two-Colorability of Nonuniform Hypergraphs}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{46:1--46:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.46},
  URN =		{urn:nbn:de:0030-drops-90505},
  doi =		{10.4230/LIPIcs.ICALP.2018.46},
  annote =	{Keywords: Property B, Nonuniform Hypergraphs, Hypergraph Coloring, Random Greedy Coloring}
}
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