A Dichotomy Theorem for Nonuniform CSPs
Andrei A. Bulatov
- pp 319-330
Reads0
Chats0
TLDR
In this paper, the authors confirm the Dichotomy Conjecture for the non-uniform CSP, which states that for every constraint language \Gm the problem is either solvable in polynomial time or is NP-complete.Abstract:
In a non-uniform Constraint Satisfaction problem CSP(Γ), where G is a set of relations on a finite set A, the goal is to find an assignment of values to variables subject to constraints imposed on specified sets of variables using the relations from Γ. The Dichotomy Conjecture for the non-uniform CSP states that for every constraint language \Gm the problem CSP(Γ) is either solvable in polynomial time or is NP-complete. It was proposed by Feder and Vardi in their seminal 1993 paper. In this paper we confirm the Dichotomy Conjecture.read more
Citations
More filters
Proceedings ArticleDOI
A Proof of CSP Dichotomy Conjecture
TL;DR: In this article, it was conjectured that if a core of a constraint language has a weak near unanimity polymorphism then the corresponding constraint satisfaction problem is tractable, unless it is NP-complete.
Proceedings ArticleDOI
Algebraic approach to promise constraint satisfaction
TL;DR: The complexity and approximability of the constraint satisfaction problem with a fixed constraint language on a finite domain has been investigated by Brakensiek and Guruswami as mentioned in this paper, who showed that for any k ≥ 3 it is NP-hard to find a (2k−1)-colouring of a given k-colourable graph.
Journal ArticleDOI
A Proof of the CSP Dichotomy Conjecture
TL;DR: This article presents an algorithm that solves Constraint Satisfaction Problem in polynomial time for constraint languages having a weak near unanimity polymorphism, which proves the remaining part of the conjecture.
Journal ArticleDOI
Equations in oligomorphic clones and the constraint satisfaction problem for ω-categorical structures
TL;DR: It is proved that any polymorphism of sufficiently large arity which is totally symmetric modulo outer embeddings of a finitely bounded structure can be turned into a non-trivial system of linear identities, and obtain non-Trivial linear identities for all tractable cases of reducts of the rational order, the random graph, and the random poset.
References
More filters
Book ChapterDOI
Recent Results on the Algebraic Approach to the CSP
TL;DR: An algebraic approach to the constraint satisfaction problem (CSP) is described and recent results on the CSP that make use of this algebraic framework are presented.
Book ChapterDOI
Dualities for Constraint Satisfaction Problems
TL;DR: An overview of logical, combinatorial, and algebraic aspects of the following forms of duality for constraint satisfaction problems: finiteDuality, bounded pathwidth duality, and bounded treewidth duality are given.
Journal ArticleDOI
On the complexity of some maltsev conditions
Ralph Freese,Matthew Valeriote +1 more
TL;DR: This paper provides sharp bounds in terms of the size of two-generated free algebras on the number of terms needed to witness various Maltsev conditions, such as congruence distributivity.
Journal ArticleDOI
The collapse of the bounded width hierarchy
TL;DR: It is shown that every constraint satisfaction problem over a fixed constraint language that has bounded relational width has also relational width (2, 3), which gives a trichotomy for width.
Proceedings ArticleDOI
A graph of a relational structure and constraint satisfaction problems
TL;DR: This paper shows how a similar edge-3-colored graph can be defined for an arbitrary finite relational structure H, and finds a solution algorithm for CSP(H), where G(H) satisfies some restrictions.
Related Papers (5)
The Computational Structure of Monotone Monadic SNP and Constraint Satisfaction: A Study through Datalog and Group Theory
Tomás Feder,Moshe Y. Vardi +1 more