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The Constraint Shortest Path (CSP) problem is as follows. An $n$-vertex graph is given, each edge/arc assigned two weights. Let us call them "cost" and "length" for definiteness. Finding a min-cost upper-bounded length path between a given…

Data Structures and Algorithms · Computer Science 2022-04-12 Adil Erzin , Roman Plotnikov , Ilya Ladygin

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

The CSP dichotomy conjecture has been recently established, but a number of other dichotomy questions remain open, including the dichotomy classification of list homomorphism problems for signed graphs. Signed graphs arise naturally in many…

Combinatorics · Mathematics 2023-03-06 Jan Bok , Richard Brewster , Pavol Hell , Nikola Jedličková , Arash Rafiey

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,…

Logic in Computer Science · Computer Science 2025-10-14 Andrei A. Bulatov , Amirhossein Kazeminia

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

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

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

A Valued Constraint Satisfaction Problem (VCSP) provides a common framework that can express a wide range of discrete optimization problems. A VCSP instance is given by a finite set of variables, a finite domain of labels, and an objective…

Computational Complexity · Computer Science 2019-04-23 Vladimir Kolmogorov

A constraint satisfaction problem (CSP) is a computational problem where the input consists of a finite set of variables and a finite set of constraints, and where the task is to decide whether there exists a satisfying assignment of values…

Computational Complexity · Computer Science 2019-04-23 Manuel Bodirsky

The role of polymorphisms in determining the complexity of constraint satisfaction problems is well established. In this context we study the stability of CSP complexity and polymorphism properties under some basic graph theoretic…

Combinatorics · Mathematics 2016-07-22 Marcel Jackson , Tomasz Kowalski , Todd Niven

The constraint satisfaction problem (CSP) involves deciding, given a set of variables and a set of constraints on the variables, whether or not there is an assignment to the variables satisfying all of the constraints. One formulation of…

Computational Complexity · Computer Science 2017-01-09 Hubie Chen , Benoit Larose

For digraphs $G$ and $H$, a homomorphism of $G$ to $H$ is a mapping $f:\ V(G)\dom V(H)$ such that $uv\in A(G)$ implies $f(u)f(v)\in A(H)$. If moreover each vertex $u \in V(G)$ is associated with costs $c_i(u), i \in V(H)$, then the cost of…

Discrete Mathematics · Computer Science 2007-10-16 Arvind Gupta , Pavol Hell , Mehdi Karimi , Arash Rafiey

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

Given a fixed constraint language $\Gamma$, the conservative CSP over $\Gamma$ (denoted by c-CSP($\Gamma$)) is a variant of CSP($\Gamma$) where the domain of each variable can be restricted arbitrarily. A dichotomy is known for conservative…

Computational Complexity · Computer Science 2016-06-21 Clément Carbonnel

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

The exponential-time hypothesis (ETH) states that 3-SAT is not solvable in subexponential time, i.e. not solvable in O(c^n) time for arbitrary c > 1, where n denotes the number of variables. Problems like k-SAT can be viewed as special…

Computational Complexity · Computer Science 2017-06-20 Peter Jonsson , Victor Lagerkvist , Biman Roy

In the field of constraint satisfaction problems (CSP), promise CSPs are an exciting new direction of study. In a promise CSP, each constraint comes in two forms: "strict" and "weak," and in the associated decision problem one must…

Data Structures and Algorithms · Computer Science 2020-12-03 Joshua Brakensiek , Venkatesan Guruswami , Marcin Wrochna , Stanislav Živný

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 if the model-complete core of the template…

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