A recent theorem of Bissacot, et al. proved using results about the cluster expansion in statistical mechanics extends the Lovász 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.
Pegden REF proved that Moser and Tardos's algorithm efficiently converges even under the condition of the cluster expansion local lemma.
An extension of the Moser-Tardos algorithmic local lemma
arXiv: Combinatorics
Mathematics Computer Science