  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.
