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A famous result by Jeavons, Cohen, and Gyssens shows that every constraint satisfaction problem (CSP) where the constraints are preserved by a semi-lattice operation can be solved in polynomial time. This is one of the basic facts for the…

Computational Complexity · Computer Science 2011-11-30 Manuel Bodirsky , Dugald Macpherson , Johan Thapper

We investigate the computational complexity of the problem of counting the maximal satisfying assignments of a Constraint Satisfaction Problem (CSP) over the Boolean domain {0,1}. A satisfying assignment is maximal if any new assignment…

Computational Complexity · Computer Science 2016-05-17 Leslie Ann Goldberg , Mark Jerrum

Constraint satisfaction problems (or CSPs) have been extensively studied in, for instance, artificial intelligence, database theory, graph theory, and statistical physics. From a practical viewpoint, it is beneficial to approximately solve…

Computational Complexity · Computer Science 2012-10-17 Tomoyuki Yamakami

The algebraic dichotomy conjecture for Constraint Satisfaction Problems (CSPs) of reducts of (infinite) finitely bounded homogeneous structures states that such CSPs are polynomial-time tractable when the model-complete core of the template…

Logic in Computer Science · Computer Science 2020-07-22 Manuel Bodirsky , Antoine Mottet , Miroslav Olšák , Jakub Opršal , Michael Pinsker , Ross Willard

A $\mu$-biased Max-CSP instance with predicate $\psi:\{0,1\}^r \to \{0,1\}$ is an instance of Constraint Satisfaction Problem (CSP) where the objective is to find a labeling of relative weight at most $\mu$ which satisfies the maximum…

Data Structures and Algorithms · Computer Science 2022-01-13 Suprovat Ghoshal , Euiwoong Lee

The problem of maximizing the $p$-th power of a $p$-norm over a halfspace-presented polytope in $\R^d$ is a convex maximization problem which plays a fundamental role in computational convexity. It has been shown in 1986 that this problem…

Computational Complexity · Computer Science 2013-07-25 Christian Knauer , Stefan König , Daniel Werner

In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to…

Artificial Intelligence · Computer Science 2011-10-12 J. Culberson , Y. Gao

Obtaining lower bounds for NP-hard problems has for a long time been an active area of research. Recent algebraic techniques introduced by Jonsson et al. (SODA 2013) show that the time complexity of the parameterized SAT($\cdot$) problem…

Computational Complexity · Computer Science 2014-06-13 Peter Jonsson , Victor Lagerkvist , Johannes Schmidt , Hannes Uppman

The quantified constraint satisfaction problem $\mathrm{QCSP}(\mathcal{A})$ is the problem to decide whether a positive Horn sentence, involving nothing more than the two quantifiers and conjunction, is true on some fixed structure…

Logic in Computer Science · Computer Science 2017-01-11 Barnaby D. Martin , Hubie Chen , Florent R. Madelaine

Constraint satisfaction problems are computational problems that naturally appear in many areas of theoretical computer science. One of the central themes is their computational complexity, and in particular the border between…

Computational Complexity · Computer Science 2026-04-28 Manuel Bodirsky

Many fundamental problems in artificial intelligence, knowledge representation, and verification involve reasoning about sets and relations between sets and can be modeled as set constraint satisfaction problems (set CSPs). Such problems…

Artificial Intelligence · Computer Science 2012-07-19 Manuel Bodirsky , Martin Hils , Alex Krimkevich

Valued constraint satisfaction problems (VCSPs) are discrete optimisation problems with a $(\mathbb{Q}\cup\{\infty\})$-valued objective function given as a sum of fixed-arity functions. In Boolean surjective VCSPs, variables take on labels…

Computational Complexity · Computer Science 2020-05-15 Peter Fulla , Hannes Uppman , Stanislav Zivny

A constraint satisfaction problem (CSP) is said to be \emph{approximation resistant} if it is hard to approximate better than the trivial algorithm which picks a uniformly random assignment. Assuming the Unique Games Conjecture, we give a…

Computational Complexity · Computer Science 2013-01-15 Per Austrin , Subhash Khot

An important question in the study of constraint satisfaction problems (CSP) is understanding how the graph or hypergraph describing the incidence structure of the constraints influences the complexity of the problem. For binary CSP…

Data Structures and Algorithms · Computer Science 2015-03-13 Dániel Marx

In this paper, we study the parameterized complexity of local search, whose goal is to find a good nearby solution from the given current solution. Formally, given an optimization problem where the goal is to find the largest feasible…

Data Structures and Algorithms · Computer Science 2025-12-04 Aditya Anand , Vincent Cohen-Addad , Tommaso d'Orsi , Anupam Gupta , Euiwoong Lee , Debmalya Panigrahi , Sijin Peng

Valued constraint satisfaction problems (VCSPs) constitute a large class of computational optimization problems. It was shown recently that, over finite domains, every VCSP is in P or NP-complete, depending on the admitted cost functions.…

Logic · Mathematics 2025-10-21 Manuel Bodirsky , Žaneta Semanišinová , Carsten Lutz

Many physical systems have underlying safety considerations that require that the policy employed ensures the satisfaction of a set of constraints. The analytical formulation usually takes the form of a Constrained Markov Decision Process…

Machine Learning · Computer Science 2021-03-03 Aria HasanzadeZonuzy , Archana Bura , Dileep Kalathil , Srinivas Shakkottai

Promise Constraint Satisfaction Problems (PCSP) were proposed recently by Brakensiek and Guruswami arXiv:1704.01937 as a framework to study approximations for Constraint Satisfaction Problems (CSP). Informally a PCSP asks to distinguish…

Computational Complexity · Computer Science 2020-03-18 Guofeng Deng , Ezzeddine El Sai , Trevor Manders , Peter Mayr , Poramate Nakkirt , Athena Sparks

Random instances of constraint satisfaction problems such as k-SAT provide challenging benchmarks. If there are m constraints over n variables there is typically a large range of densities r=m/n where solutions are known to exist with…

Discrete Mathematics · Computer Science 2009-11-13 Amin Coja-Oghlan

A conservative class of constraint satisfaction problems CSPs is a class for which membership is preserved under arbitrary domain reductions. Many well-known tractable classes of CSPs are conservative. It is well known that lexleader…

Artificial Intelligence · Computer Science 2015-03-17 Tim januschowski , Barbara M. Smith , M. R. C. van Dongen