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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The Power of the Combined Basic LP and Affine Relaxation for Promise CSPs.
TL;DR: A simple algorithm which in polynomial time solves the decision problem for all promise CSPs that admit infinitely many symmetric polymorphisms, that is the coordinates are permutation invariant, and it is shown that block symmetrical polymorphisms are not only sufficient but also necessary for this algorithm to work, thus establishing its precise power.
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A Proof of the CSP Dichotomy Conjecture
TL;DR: In this paper, a polynomial time algorithm for constraint languages having a weak near unanimity polymorphism was presented, which proved the remaining part of the conjecture, and showed that the constraint satisfaction problem is tractable in such constraint languages.
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Bi-Arc Digraphs and Conservative Polymorphisms
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Kernelization of Constraint Satisfaction Problems: A Study Through Universal Algebra
TL;DR: An algebraic approach is taken to the problem of characterizing the kernelization limits of NP-hard CSP problems, parameterized by the number of variables, and gives indication that the Maltsev condition might be a complete characterization for Boolean CSPs with linear kernels.
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Finitely Tractable Promise Constraint Satisfaction Problems
Kristina Asimi,Libor Barto +1 more
TL;DR: This work begins a systematic study of this phenomenon by giving a general necessary condition for finite tractability and characterizing finite tractable within a class of templates - the "basic" tractable cases in the dichotomy theorem for symmetric Boolean PCSPs allowing negations by Brakensiek and Guruswami.
References
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