Constraint satisfaction problems over semilattice block Mal'tsev algebras

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 σ such that the quotient A/ σ with operation f is a semilattice, f is a projection on every block of σ, and every block of σ 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.