Decimation flows in constraint satisfaction problems

TL;DR

This paper introduces a novel decimation algorithm for constraint satisfaction problems that leverages the transformation of constraints into linear forms, significantly improving performance on complex problems.

Contribution

The paper presents a new decimation method exploiting linear structures in problems, enabling efficient solving when the flow reaches linear subspaces.

Findings

Enhanced performance on locked occupation problems

Effective use of Gaussian elimination at linear subspaces

Decimation flow transforms constraints into linear forms

Abstract

We study hard constraint satisfaction problems with a decimation approach based on message passing algorithms. Decimation induces a renormalization flow in the space of problems, and we exploit the fact that this flow transforms some of the constraints into linear constraints over GF(2). In particular, when the flow hits the subspace of linear problems, one can stop decimation and use Gaussian elimination. We introduce a new decimation algorithm which uses this linear structure and shows a strongly improved performance with respect to the usual decimation methods on some of the hardest locked occupation problems.