Binarisation for Valued Constraint Satisfaction Problems

TL;DR

This paper explores methods to convert valued constraint satisfaction problems into binary forms, preserving algebraic properties and establishing polynomial-time equivalences with known problems, advancing the understanding of VCSP complexity.

Contribution

It introduces a dual encoding that maintains algebraic properties and extends CSP binary reduction techniques to VCSPs, linking them to Minimum-Cost Homomorphism Problems.

Findings

Dual encoding preserves algebraic properties of VCSPs

Reduction of VCSPs to binary form is polynomial-time equivalent to known problems

Establishes connections between VCSPs and Minimum-Cost Homomorphism Problems

Abstract

We study methods for transforming valued constraint satisfaction problems (VCSPs) to binary VCSPs. First, we show that the standard dual encoding preserves many aspects of the algebraic properties that capture the computational complexity of VCSPs. Second, we extend the reduction of CSPs to binary CSPs described by Bulin et al. [LMCS'15] to VCSPs. This reduction establishes that VCSPs over a fixed valued constraint language are polynomial-time equivalent to Minimum-Cost Homomorphism Problems over a fixed digraph.