A Dichotomy Theorem for Nonuniform CSPs
Andrei A. Bulatov
- pp 319-330
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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
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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.
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Absorbing subalgebras, cyclic terms, and the constraint satisfaction problem ∗
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The Dichotomy for Conservative Constraint Satisfaction Problems Revisited
TL;DR: This paper provides a short and transparent proof of the dichotomy conjecture of Feder and Vardi stating that the CSP over a fixed constraint language is either NP-complete, or tractable.
Proceedings Article
A Game-Theoretic Approach to Constraint Satisfaction
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