A Dichotomy Theorem for Nonuniform CSPs

In a non-uniform Constraint Satisfaction problem CSP(Γ), where Γ is a set of relations on a unite set A, the goal is to und an assignment of values to variables subject to constraints imposed on speciued sets of variables using the relations from Γ. The Dichotomy Conjecture for the non-uniform CSP states that for every constraint language Γ 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.