58 Search Results for "Živný, Stanislav"

Volume

Dagstuhl Follow-Ups, Volume 7

The Constraint Satisfaction Problem: Complexity and Approximability

Editors: Andrei Krokhin and Stanislav Zivny

Document
DOI: 10.4230/LIPIcs.SEA.2026.3
Approximation Algorithms for Budget Splitting in Multi-Channel Influence Maximization

Authors: Dildar Ali, Ansh Jasrotia, Abishek Salaria, and Suman Banerjee

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract
How to utilize an allocated budget effectively for branding and promotion of a commercial house is an important problem, particularly when multiple advertising media are available. There exist multiple such media, and among them, two popular ones are billboards and social media advertisements. In this context, the question naturally arises: how should a budget be allocated to maximize total influence? Although there is significant literature on the effective use of budgets in individual advertising media, there are hardly any studies examining budget allocation across multiple advertising media. To bridge this gap, this paper introduces the Budget Splitting Problem in Billboard and Social Network Advertisement. We introduce the notion of interaction effect to capture the additional influence due to triggers from multiple media of advertising. Using this notion, we propose a noble influence function Φ(,) that captures the total influence and shows that this function is non-negative, monotone, and non-bisubmodular. We introduce bi-submodularity ratio (γ) and generalized curvature (α) to measure how close a function is to being bi-submodular and how far a function is from being modular, respectively. We propose the Randomized Greedy and Two-Phase Adaptive Greedy approach, where the influence function is non-bisubmodular and achieves an approximation guarantee of (1/α)(1-e^(-γα)). We conducted several experiments using real-world datasets and observed that the proposed solution approach’s budget splitting leads to a greater influence than existing approaches.
Cite as

Dildar Ali, Ansh Jasrotia, Abishek Salaria, and Suman Banerjee. Approximation Algorithms for Budget Splitting in Multi-Channel Influence Maximization. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 3:1-3:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ali_et_al:LIPIcs.SEA.2026.3,
  author =	{Ali, Dildar and Jasrotia, Ansh and Salaria, Abishek and Banerjee, Suman},
  title =	{{Approximation Algorithms for Budget Splitting in Multi-Channel Influence Maximization}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{3:1--3:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.3},
  URN =		{urn:nbn:de:0030-drops-260070},
  doi =		{10.4230/LIPIcs.SEA.2026.3},
  annote =	{Keywords: Advertisement, Billboard, Social Network, Bi-submodularity, Influence Maximization}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.22
Search-Space Reduction for Boolean MinCSPs via Essential Constraints

Authors: Bart M. P. Jansen and Ruben F. A. Verhaegh

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
For a fixed set ℱ of Boolean constraint types, a MinCSP(ℱ)-instance consists of a formula F that applies m constraints from ℱ to a set of n Boolean variables. The goal is to remove a minimum subset of constraint applications from F to make the remaining formula satisfiable. Previous work characterized how the choice of ℱ affects its polynomial-time solvability and approximability. We extend a recently introduced preprocessing framework for graph problems to the problem above. Rephrased in the context of CSPs, this framework defines a constraint application from a given formula F as c-essential if it is contained in all c-approximate solutions to F. Being able to efficiently detect these essential parts of a solution reduces the search space of any follow-up FPT algorithms parameterized by the solution size and yields an immediate asymptotic improvement to the runtime of such algorithms. In this work, we present a dichotomy theorem that distinguishes constraint sets ℱ for which c_ℱ-essential constraint applications can be detected efficiently for some c_{ℱ} ∈ 𝒪(1), from those for which this task is intractable under established complexity-theoretic conjectures. Our results show that for any set ℱ of bijunctive constraints, there is a polynomial-time algorithm that detects 𝒪(1)-essential constraint applications. This contrasts the fact that constant-factor approximating a bijunctive MinCSP(ℱ)-problem is intractable under the Unique Games Conjecture.
Cite as

Bart M. P. Jansen and Ruben F. A. Verhaegh. Search-Space Reduction for Boolean MinCSPs via Essential Constraints. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 22:1-22:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{jansen_et_al:LIPIcs.SWAT.2026.22,
  author =	{Jansen, Bart M. P. and Verhaegh, Ruben F. A.},
  title =	{{Search-Space Reduction for Boolean MinCSPs via Essential Constraints}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{22:1--22:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.22},
  URN =		{urn:nbn:de:0030-drops-260586},
  doi =		{10.4230/LIPIcs.SWAT.2026.22},
  annote =	{Keywords: fixed-parameter tractability, constraint satisfaction problems}
}
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.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.CSL.2026.9
Arity Hierarchies for Quantifiers Closed Under Partial Polymorphisms

Authors: Anuj Dawar, Lauri Hella, and Benedikt Pago

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
We investigate the expressive power of generalized quantifiers closed under partial polymorphism conditions motivated by the study of constraint satisfaction problems. We answer a number of questions arising from the work of Dawar and Hella (CSL 2024) where such quantifiers were introduced. For quantifiers closed under partial near-unanimity polymorphisms, we establish hierarchy results clarifying the interplay between the arity of the polymorphisms and of the quantifiers: The expressive power of (𝓁+1)-ary quantifiers closed under 𝓁-ary partial near-unanimity polymorphisms is strictly between the class of all quantifiers of arity 𝓁-1 and 𝓁. We also establish an infinite hierarchy based on the arity of quantifiers with a fixed arity of partial near-unanimity polymorphisms. Finally, we prove inexpressiveness results for quantifiers with a partial Maltsev polymorphism. The separation results are proved using novel algebraic constructions in the style of Cai-Fürer-Immerman and the quantifier pebble games of Dawar and Hella (2024).
Cite as

Anuj Dawar, Lauri Hella, and Benedikt Pago. Arity Hierarchies for Quantifiers Closed Under Partial Polymorphisms. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{dawar_et_al:LIPIcs.CSL.2026.9,
  author =	{Dawar, Anuj and Hella, Lauri and Pago, Benedikt},
  title =	{{Arity Hierarchies for Quantifiers Closed Under Partial Polymorphisms}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.9},
  URN =		{urn:nbn:de:0030-drops-254330},
  doi =		{10.4230/LIPIcs.CSL.2026.9},
  annote =	{Keywords: finite model theory, constraint satisfaction problems, generalized quantifiers}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.11
Classical and Quantum Polynomial Freiman-Ruzsa Algorithms

Authors: Srinivasan Arunachalam, Davi Castro-Silva, Arkopal Dutt, and Tom Gur

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We prove algorithmic versions of the polynomial Freiman-Ruzsa theorem of Gowers, Green, Manners, and Tao (Annals of Mathematics, 2025) in additive combinatorics. In particular, we give classical and quantum polynomial-time algorithms that, for A ⊆ 𝔽₂ⁿ with doubling constant K, learn an explicit description of a subspace V ⊆ 𝔽₂ⁿ of size |V| ≤ |A| such that A can be covered by K^C translates of V, for a universal constant C > 1.
Cite as

Srinivasan Arunachalam, Davi Castro-Silva, Arkopal Dutt, and Tom Gur. Classical and Quantum Polynomial Freiman-Ruzsa Algorithms. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 11:1-11:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{arunachalam_et_al:LIPIcs.ITCS.2026.11,
  author =	{Arunachalam, Srinivasan and Castro-Silva, Davi and Dutt, Arkopal and Gur, Tom},
  title =	{{Classical and Quantum Polynomial Freiman-Ruzsa Algorithms}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{11:1--11:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.11},
  URN =		{urn:nbn:de:0030-drops-252987},
  doi =		{10.4230/LIPIcs.ITCS.2026.11},
  annote =	{Keywords: Additive combinatorics, sublinear algorithms}
}
Document
DOI: 10.4230/DagRep.15.5.114
The Constraint Satisfaction Problem: Complexity and Approximability (Dagstuhl Seminar 25211)

Authors: Manuel Bodirsky, Venkatesan Guruswami, Dániel Marx, Stanislav Živný, and Žaneta Semanišinová

Published in: Dagstuhl Reports, Volume 15, Issue 5 (2025)

Abstract
Constraint satisfaction has always played a central role in computational complexity theory; appropriate versions of CSPs are classical complete problems for most standard complexity classes. CSPs constitute a very rich and yet sufficiently manageable class of problems to give a good perspective on general computational phenomena. For instance, they help to understand which mathematical properties make a computational problem tractable (in a wide sense, e.g., polynomial-time solvable, non-trivially approximable, etc.). One of the most striking features of this research direction is the variety of different branches of mathematics (including algebra and logic, combinatorics and graph theory, probability theory and mathematical programming, and most recently topology) that are used to achieve deep insights in the study of the CSP, and this seminar will contribute towards further synergy in the area. In the last 20 years, research activity in this area has significantly intensified and hugely impressive progress was made. The Dagstuhl Seminar 25211 "The Constraint Satisfaction Problem: Complexity and Approximability" was aimed at bringing together researchers using all the different techniques in the study of the CSP so that they can share their insights obtained during the past four years. This report documents the material presented during the course of the seminar.
Cite as

Manuel Bodirsky, Venkatesan Guruswami, Dániel Marx, Stanislav Živný, and Žaneta Semanišinová. The Constraint Satisfaction Problem: Complexity and Approximability (Dagstuhl Seminar 25211). In Dagstuhl Reports, Volume 15, Issue 5, pp. 114-133, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{bodirsky_et_al:DagRep.15.5.114,
  author =	{Bodirsky, Manuel and Guruswami, Venkatesan and Marx, D\'{a}niel and \v{Z}ivn\'{y}, Stanislav and Semani\v{s}inov\'{a}, \v{Z}aneta},
  title =	{{The Constraint Satisfaction Problem: Complexity and Approximability (Dagstuhl Seminar 25211)}},
  pages =	{114--133},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2025},
  volume =	{15},
  number =	{5},
  editor =	{Bodirsky, Manuel and Guruswami, Venkatesan and Marx, D\'{a}niel and \v{Z}ivn\'{y}, Stanislav and Semani\v{s}inov\'{a}, \v{Z}aneta},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.15.5.114},
  URN =		{urn:nbn:de:0030-drops-252762},
  doi =		{10.4230/DagRep.15.5.114},
  annote =	{Keywords: computational complexity, constraint satisfaction problem, hardness of approximation, parameterized complexity, semidefinite programming}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.3
Maximum And- vs. Even-SAT

Authors: Tamio-Vesa Nakajima and Stanislav Živný

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

Abstract
A multiset of literals, called a clause, is strongly satisfied by an assignment if no literal evaluates to false. Finding an assignment that maximises the number of strongly satisfied clauses is NP-hard. We present a simple algorithm that finds, given a multiset of clauses that admits an assignment that strongly satisfies ρ of the clauses, an assignment in which at least ρ of the clauses are weakly satisfied, in the sense that an even number of literals evaluate to false. In particular, this implies an efficient algorithm for finding an undirected cut of value ρ in a graph G given that a directed cut of value ρ in G is promised to exist. A similar argument also gives an efficient algorithm for finding an acyclic subgraph of G with ρ edges under the same promise.
Cite as

Tamio-Vesa Nakajima and Stanislav Živný. Maximum And- vs. Even-SAT. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 3:1-3:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{nakajima_et_al:LIPIcs.APPROX/RANDOM.2025.3,
  author =	{Nakajima, Tamio-Vesa and \v{Z}ivn\'{y}, Stanislav},
  title =	{{Maximum And- vs. Even-SAT}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{3:1--3:8},
  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.2025.3},
  URN =		{urn:nbn:de:0030-drops-243696},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.3},
  annote =	{Keywords: approximation, promise constraint satisfaction, max and, max even, max cut, max dicut, max acyclic}
}
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.2025.37
New Hardness Results for Low-Rank Matrix Completion

Authors: Dror Chawin and Ishay Haviv

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

Abstract
The low-rank matrix completion problem asks whether a given real matrix with missing values can be completed so that the resulting matrix has low rank or is close to a low-rank matrix. The completed matrix is often required to satisfy additional structural constraints, such as positive semi-definiteness or a bounded infinity norm. The problem arises in various research fields, including machine learning, statistics, and theoretical computer science, and has broad real-world applications. This paper presents new NP-hardness results for low-rank matrix completion problems. We show that for every sufficiently large integer d and any real number ε ∈ [2^{-O(d)},1/7], given a partial matrix A with exposed values of magnitude at most 1 that admits a positive semi-definite completion of rank d, it is NP-hard to find a positive semi-definite matrix that agrees with each given value of A up to an additive error of at most ε, even when the rank is allowed to exceed d by a multiplicative factor of O (1/(ε²⋅log(1/ε))). This strengthens a result of Hardt, Meka, Raghavendra, and Weitz (COLT, 2014), which applies to multiplicative factors smaller than 2 and to ε that decays polynomially in d. We establish similar NP-hardness results for the case where the completed matrix is constrained to have a bounded infinity norm (rather than be positive semi-definite), for which all previous hardness results rely on complexity assumptions related to the Unique Games Conjecture. Our proofs involve a novel notion of nearly orthonormal representations of graphs, the concept of line digraphs, and bounds on the rank of perturbed identity matrices.
Cite as

Dror Chawin and Ishay Haviv. New Hardness Results for Low-Rank Matrix Completion. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 37:1-37:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chawin_et_al:LIPIcs.MFCS.2025.37,
  author =	{Chawin, Dror and Haviv, Ishay},
  title =	{{New Hardness Results for Low-Rank Matrix Completion}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{37:1--37:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.37},
  URN =		{urn:nbn:de:0030-drops-241448},
  doi =		{10.4230/LIPIcs.MFCS.2025.37},
  annote =	{Keywords: hardness of approximation, low-rank matrix completion, graph coloring}
}
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}
}
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