A dichotomy theorem for nonuniform CSPs simplified

TL;DR

This paper confirms the Dichotomy Conjecture for non-uniform CSPs, establishing that each such problem is either solvable in polynomial time or NP-complete, thus resolving a long-standing open problem in computational complexity.

Contribution

The paper proves the Dichotomy Conjecture for non-uniform CSPs, providing a complete classification of their computational complexity.

Findings

Confirmed the Dichotomy Conjecture for non-uniform CSPs

Classified all non-uniform CSPs as either polynomial-time solvable or NP-complete

Resolved a major open problem in the complexity theory of constraint satisfaction problems

Abstract

In a non-uniform Constraint Satisfaction problem CSP(G), 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 G. The Dichotomy Conjecture for the non-uniform CSP states that for every constraint language G the problem CSP(G) 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.