Constraint Satisfaction Problems over semilattice block Mal'tsev algebras

Andrei A. Bulatov

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arXiv · 1701.02623

Constraint Satisfaction Problems over semilattice block Mal'tsev algebras

Andrei A. Bulatov

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Abstract

There are two well known types of algorithms for solving CSPs: local propagation and generating a basis of the solution space. For several years the focus of the CSP research has been on `hybrid' algorithms that somehow combine the two approaches. In this paper we present a new method of such hybridization that allows us to solve certain CSPs that has been out of reach for a quite a while. We consider these method on a fairly restricted class of CSPs given by algebras we will call semilattice block Mal'tsev. An algebra A is called semilattice block Mal'tsev if it has a binary operation f, a ternary operation m, and a congruence s such that the quotient A/s with operation $f$ is a semilattice, $f$ is a projection on every block of s, and every block of s is a Mal'tsev algebra with Mal'tsev operation m. We show that the constraint satisfaction problem over a semilattice block Mal'tsev algebra is solvable in polynomial time.

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Andrei A. Bulatov. 2017-01-10. Constraint Satisfaction Problems over semilattice block Mal'tsev algebras. https://arxiv.org/abs/1701.02623

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