The combined basic LP and affine IP relaxation for promise VCSPs on infinite domains

TL;DR

This paper extends a known tractability result to promise valued CSPs over infinite domains by combining basic LP and affine IP relaxations, advancing the understanding of solvability in complex CSP generalizations.

Contribution

It provides a sufficient condition for exact solvability of promise valued CSPs on infinite domains using combined LP and affine IP relaxations, generalizing prior finite-domain results.

Findings

Extended tractability results to infinite domains.

Identified conditions for exact solvability using combined relaxations.

Bridged gap between finite and infinite domain CSPs.

Abstract

Convex relaxations have been instrumental in solvability of constraint satisfaction problems (CSPs), as well as in the three different generalisations of CSPs: valued CSPs, infinite-domain CSPs, and most recently promise CSPs. In this work, we extend an existing tractability result to the three generalisations of CSPs combined: We give a sufficient condition for the combined basic linear programming and affine integer programming relaxation for exact solvability of promise valued CSPs over infinite-domains. This extends a result of Brakensiek and Guruswami [SODA'20] for promise (non-valued) CSPs (on finite domains).