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Constraint satisfaction problems (CSPs) for first-order reducts of finitely bounded homogeneous structures form a large class of computational problems that might exhibit a complexity dichotomy, P versus NP-complete. A powerful method to…

Logic · Mathematics 2024-05-13 Manuel Bodirsky , Bertalan Bodor

Finite valued constraint satisfaction problems are a formalism for describing many natural optimization problems, where constraints on the values that variables can take come with rational weights and the aim is to find an assignment of…

Logic in Computer Science · Computer Science 2015-04-15 Anuj Dawar , Pengming Wang

We consider the problem of satisfiability of sets of constraints in a given set of finite uniform hypergraphs. While the problem under consideration is similar in nature to the problem of satisfiability of constraints in graphs, the…

Logic in Computer Science · Computer Science 2025-08-25 Antoine Mottet , Tomáš Nagy , Michael Pinsker

The constraint satisfaction problem (CSP) is concerned with homomorphisms between two structures. For CSPs with restricted left-hand side structures, the results of Dalmau, Kolaitis, and Vardi [CP'02], Grohe [FOCS'03/JACM'07], and Atserias,…

Computational Complexity · Computer Science 2022-02-02 Clement Carbonnel , Miguel Romero , Stanislav Zivny

We consider the problem of finding a homomorphism from an input digraph $G$ to a fixed digraph $H$. We show that if $H$ admits a weak-near-unanimity polymorphism $\phi$ then deciding whether $G$ admits a homomorphism to $H$ (HOM($H$)) is…

Computational Complexity · Computer Science 2020-08-11 Tomás Feder , Jeff Kinne , Ashwin Murali , Arash Rafiey

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

We study the Constraint Satisfaction Problem CSP(A), where A is first-order definable in (Z;+,1) and contains +. We prove such problems are either in P or NP-complete.

Computational Complexity · Computer Science 2018-07-04 Manuel Bodirsky , Barnaby Martin , Marcello Mamino , Antoine Mottet

A classic result due to Schaefer (1978) classifies all constraint satisfaction problems (CSPs) over the Boolean domain as being either in $\mathsf{P}$ or $\mathsf{NP}$-hard. This paper considers a promise-problem variant of CSPs called…

Computational Complexity · Computer Science 2021-05-07 Joshua Brakensiek , Venkatesan Guruswami

The constraint satisfaction problem asks to decide if a set of constraints over a relational structure $\mathcal{A}$ is satisfiable (CSP$(\mathcal{A})$). We consider CSP$(\mathcal{A} \cup \mathcal{B})$ where $\mathcal{A}$ is a structure and…

Computational Complexity · Computer Science 2024-08-28 Peter Jonsson , Victor Lagerkvist , George Osipov

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

To any fixed, finite relational structure, $\mathbb{D}$, there is an associated decision problem, CSP$(\mathbb{D})$, which is a restricted version of the constraint satisfaction problem. In [8], the so called "algebraic approach" to the…

Logic · Mathematics 2016-09-14 Ian Payne

Although the CSP (constraint satisfaction problem) is NP-complete, even in the case when all constraints are binary, certain classes of instances are tractable. We study classes of instances defined by excluding subproblems. This approach…

Artificial Intelligence · Computer Science 2012-01-19 Martin C. Cooper , Guillaume Escamocher

A computational problem exhibits a "gap property" when there is no tractable boundary between two disjoint sets of instances. We establish a Gap Trichotomy Theorem for a family of constraint problem variants, completely classifying the…

Computational Complexity · Computer Science 2017-03-28 Lucy Ham

We study parameterized Constraint Satisfaction Problem for infinite constraint languages. The parameters that we study are weight of the satisfying assignment, number of constraints, maximum number of occurrences of a variable in the…

Computational Complexity · Computer Science 2017-08-10 Ruhollah Majdoddin

Building on a result of Larose and Tesson for constraint satisfaction problems (CSP s), we uncover a dichotomy for the quantified constraint satisfaction problem QCSP(B), where B is a finite structure that is a core. Specifically, such…

Computational Complexity · Computer Science 2011-02-18 Barnaby Martin

It is well known that the constraint satisfaction problem over a general relational structure A is polynomial time equivalent to the constraint problem over some associated digraph. We present a variant of this construction and show that…

Computational Complexity · Computer Science 2017-01-11 Jakub Bulín , Dejan Delic , Marcel Jackson , Todd Niven

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

The Dichotomy Conjecture for constraint satisfaction problems (CSPs) states that every CSP is in P or is NP-complete (Feder-Vardi, 1993). It has been verified for conservative problems (also known as list homomorphism problems) by A.…

Computational Complexity · Computer Science 2013-08-02 Laszlo Egri , Pavol Hell , Benoit Larose , Arash Rafiey

This paper focuses on the algebraic theory underlying the study of the complexity and the algorithms for the Constraint Satisfaction Problem (CSP). We unify, simplify, and extend parts of the three approaches that have been developed to…

Computational Complexity · Computer Science 2024-08-07 Libor Barto , Zarathustra Brady , Andrei Bulatov , Marcin Kozik , Dmitriy Zhuk

A Boolean constraint satisfaction instance is a conjunction of constraint applications, where the allowed constraints are drawn from a fixed set B of Boolean functions. We consider the problem of determining whether two given constraint…

Computational Complexity · Computer Science 2007-05-23 E. Boehler , E. Hemaspaandra , Steffen Reith , Heribert Vollmer