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Related papers: The Complexity of General-Valued CSPs

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We study optimisation problems that can be formulated as valued constraint satisfaction problems (VCSP). A problem from VCSP is characterised by a \emph{constraint language}, a fixed set of cost functions taking finite and infinite costs…

Computational Complexity · Computer Science 2010-08-19 Vladimir Kolmogorov , Stanislav Zivny

Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…

Computational Complexity · Computer Science 2020-10-05 Dmitriy Zhuk

A finite constraint language $\mathscr{R}$ is a finite set of relations over some finite domain $A$. We show that intractability of the constraint satisfaction problem $\operatorname{CSP}(\mathscr{R})$ can, in all known cases, be replaced…

Computational Complexity · Computer Science 2017-05-02 Lucy Ham , Marcel Jackson

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

We give a complexity dichotomy theorem for the counting Constraint Satisfaction Problem (#CSP in short) with complex weights. To this end, we give three conditions for its tractability. Let F be any finite set of complex-valued functions,…

Computational Complexity · Computer Science 2015-03-19 Jin-Yi Cai , Xi Chen

A Constraint Satisfaction Problem (CSP) is a computational problem where we are given variables and constraints about them; the question is whether the variables can be assigned values such that all constraints are satisfied. We give an…

Logic in Computer Science · Computer Science 2022-04-01 Michael Pinsker

An instance of Max CSP is a finite collection of constraints on a set of variables, and the goal is to assign values to the variables that maximises the number of satisfied constraints. Max CSP captures many well-known problems (such as Max…

Computational Complexity · Computer Science 2007-12-11 Peter Jonsson , Andrei Krokhin , Fredrik Kuivinen

Valued constraint satisfaction problems (VCSPs) are a large class of combinatorial optimisation problems. The computational complexity of VCSPs depends on the set of allowed cost functions in the input. Recently, the computational…

Logic in Computer Science · Computer Science 2022-04-04 Manuel Bodirsky , Marcello Mamino , Caterina Viola

The Constraint Satisfaction Problem (CSP) is a central and generic computational problem which provides a common framework for many theoretical and practical applications. A central line of research is concerned with the identification of…

Data Structures and Algorithms · Computer Science 2015-07-21 Robert Ganian , M. S. Ramanujan , Stefan Szeider

A counting constraint satisfaction problem (#CSP) asks for the number of ways to satisfy a given list of constraints, drawn from a fixed constraint language \Gamma. We study how hard it is to evaluate this number approximately. There is an…

Computational Complexity · Computer Science 2012-04-26 Colin McQuillan

Constraint satisfaction problem (CSP) is a well-studied combinatorial search problem, in which we are asked to find an assignment of values to given variables so as to satisfy all of given constraints. We study a reconfiguration variant of…

Data Structures and Algorithms · Computer Science 2018-12-31 Tatsuhiko Hatanaka , Takehiro Ito , Xiao Zhou

Constraint satisfaction problems (CSPs) consist of a set of variables taking values from some finite domain and a set of local constraints on these variables. The objective is to find an assignment to the variables that maximizes the…

Computational Complexity · Computer Science 2026-05-12 Amey Bhangale , Yezhou Zhang

We study the computational complexity of planar valued constraint satisfaction problems (VCSPs), which require the incidence graph of the instance be planar. First, we show that intractable Boolean VCSPs have to be self-complementary to be…

Computational Complexity · Computer Science 2017-04-12 Peter Fulla , Stanislav Zivny

Constraint satisfaction problems (CSPs) are a natural class of decision problems where one must decide whether there is an assignment to variables that satisfies a given formula. Schaefer's dichotomy theorem, and its extension to all…

Quantum Physics · Physics 2025-02-27 Eric Culf , Kieran Mastel

The constraint satisfaction probem (CSP) is a well-acknowledged framework in which many combinatorial search problems can be naturally formulated. The CSP may be viewed as the problem of deciding the truth of a logical sentence consisting…

Logic in Computer Science · Computer Science 2007-05-23 Hubie Chen

We study the complexity of the valued constraint satisfaction problem (VCSP) for every valued structure with the domain ${\mathbb Q}$ that is preserved by all order-preserving bijections. Such VCSPs will be called temporal, in analogy to…

Logic · Mathematics 2026-01-21 Manuel Bodirsky , Édouard Bonnet , Žaneta Semanišinová

We report new results on the complexity of the valued constraint satisfaction problem (VCSP). Under the unique games conjecture, the approximability of finite-valued VCSP is fairly well-understood. However, there is yet no characterisation…

Computational Complexity · Computer Science 2011-04-29 Peter Jonsson , Fredrik Kuivinen , Johan Thapper

We determine the computational complexity of approximately counting the total weight of variable assignments for every complex-weighted Boolean constraint satisfaction problem (or CSP) with any number of additional unary (i.e., arity 1)…

Computational Complexity · Computer Science 2015-05-19 Tomoyuki Yamakami

In the constraint satisfaction problem ($CSP$), the aim is to find an assignment of values to a set of variables subject to specified constraints. In the minimum cost homomorphism problem ($MinHom$), one is additionally given weights…

Machine Learning · Computer Science 2010-04-06 Rustem Takhanov

The paper presents an algebraic framework for optimization problems expressible as Valued Constraint Satisfaction Problems. Our results generalize the algebraic framework for the decision version (CSPs) provided by Bulatov et al. [SICOMP…

Computational Complexity · Computer Science 2016-05-03 Marcin Kozik , Joanna Ochremiak