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A Dichotomy Theorem for Nonuniform CSPs

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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.

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QCSP on Reflexive Tournaments

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References
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Proceedings ArticleDOI

The complexity of satisfiability problems

TL;DR: An infinite class of satisfiability problems is considered which contains these two particular problems as special cases, and it is shown that every member of this class is either polynomial-time decidable or NP-complete.
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The Computational Structure of Monotone Monadic SNP and Constraint Satisfaction: A Study through Datalog and Group Theory

TL;DR: This paper isolates a class (of problems specified by) "monotone monadic SNP without inequality" which may exhibit a dichotomy, and explains the placing of all these restrictions by showing, essentially using Ladner's theorem, that classes obtained by using only two of the above three restrictions do not show this dichotomy.
Journal ArticleDOI

On the complexity of H -coloring

TL;DR: The natural conjecture, formulated in several sources, asserts that the H-coloring problem is NP-complete for any non-bipartite graph H, and a proof of this conjecture is given.
Journal ArticleDOI

Classifying the Complexity of Constraints Using Finite Algebras

TL;DR: It is shown that any set of relations used to specify the allowed forms of constraints can be associated with a finite universal algebra and how the computational complexity of the corresponding constraint satisfaction problem is connected to the properties of this algebra is explored.
Journal ArticleDOI

Undirected connectivity in log-space

TL;DR: A deterministic, log-space algorithm that solves st-connectivity in undirected graphs and implies a way to construct in log- space a fixed sequence of directions that guides a deterministic walk through all of the vertices of any connected graph.
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