The Moser-Tardos Framework with Partial Resampling

The resampling algorithm of Moser & Tardos is a powerful approach to develop versions of the Lovasz Local Lemma. We develop a partial resampling approach motivated by this methodology: when a bad event holds, we resample an appropriately-random subset of the set of variables that define this event, rather than the entire set as in Moser & Tardos. This leads to several improved algorithmic applications in scheduling, graph transversals, packet routing etc. For instance, we improve the approximation ratio of a generalized D-dimensional scheduling problem studied by Azar & Epstein from O(D) to O(log D/ log log D), and settle a conjecture of Szabo & Tardos on graph transversals asymptotically.