CSP for binary conservative relational structures

TL;DR

This paper characterizes the computational complexity of CSPs for certain binary conservative relational structures, showing they are either NP-complete or have bounded width, based on their algebraic properties.

Contribution

It establishes a dichotomy for CSPs of 3-conservative structures with binary and unary relations, linking algebraic properties to computational complexity.

Findings

CSPs for these structures are either NP-complete or have bounded width.

The algebra of polymorphisms either lacks a Taylor operation or generates a congruence meet semidistributive variety.

Abstract

We prove that whenever A is a 3-conservative relational structure with only binary and unary relations then the algebra of polymorphisms of A either has no Taylor operation (i.e. CSP(A) is NP-complete), or generates a congruence meet semidistributive variety (i.e. CSP(A) has bounded width).