Moser-Tardos resampling algorithm, entropy compression method and the subset gas

TL;DR

This paper links the entropy compression method with the Moser-Tardos resampling algorithm via the cluster expansion of the subset gas, showing they yield identical bounds and establishing a theoretical connection.

Contribution

It introduces a novel connection between entropy compression and the Moser-Tardos algorithm through the subset gas cluster expansion, unifying two approaches.

Findings

Entropy compression and Moser-Tardos algorithms produce identical bounds.

A theoretical link between entropy methods and local lemma algorithms is established.

The cluster expansion of the subset gas is key to connecting these methods.

Abstract

We establish a connection between the entropy compression method and the Moser-Tardos algorithmic version of the Lov\'asz local lemma through the cluster expansion of the subset gas. We also show that the Moser-Tardos resampling algorithm and the entropy compression bactracking algorithm produce identical bounds.