On the reduction of the CSP dichotomy conjecture to digraphs

TL;DR

This paper demonstrates that the algebraic dichotomy conjecture for CSPs can be reduced to digraphs in logspace, preserving key properties like bounded width, thus simplifying the conjecture's analysis.

Contribution

It introduces a simple, logspace-preserving reduction from general CSPs to digraphs, showing the equivalence of the algebraic dichotomy conjecture to its digraph restriction.

Findings

Reduction preserves bounded width property

Reduction is computable in logspace

Dichotomy conjecture equivalence to digraph case

Abstract

It is well known that the constraint satisfaction problem over general relational structures can be reduced in polynomial time to digraphs. We present a simple variant of such a reduction and use it to show that the algebraic dichotomy conjecture is equivalent to its restriction to digraphs and that the polynomial reduction can be made in logspace. We also show that our reduction preserves the bounded width property, i.e., solvability by local consistency methods. We discuss further algorithmic properties that are preserved and related open problems.