An extension of the Moser-Tardos algorithmic local lemma

TL;DR

This paper extends the Moser-Tardos algorithmic local lemma to incorporate a recent theorem that weakens the conditions of the Lovász Local Lemma, using an approach inspired by statistical mechanics.

Contribution

It provides an algorithmic version of a new theorem that broadens the applicability of the local lemma, with an alternative proof within the Moser-Tardos framework.

Findings

Extended the Moser-Tardos algorithmic local lemma to new conditions.

Provided an alternative proof of Bissacot et al.'s theorem.

Broadened the scope of algorithmic local lemma applications.

Abstract

A recent theorem of Bissacot, et al. proved using results about the cluster expansion in statistical mechanics extends the Lov\'asz Local Lemma by weakening the conditions under which its conclusions holds. In this note, we prove an algorithmic analog of this result, extending Moser and Tardos's recent algorithmic Local Lemma, and providing an alternative proof of the theorem of Bissacot, et al. applicable in the Moser-Tardos algorithmic framework.