Abstract
The resampling algorithm of Moser and Tardos is a powerful approach to develop constructive versions of the Lovász Local Lemma. We generalize this to partial resampling: When a bad event holds, we resample an appropriately random subset of the variables that define this event rather than the entire set, as in Moser and Tardos. This is particularly useful when the bad events are determined by sums of random variables. This leads to several improved algorithmic applications in scheduling, graph transversals, packet routing, and so on. For instance, we settle a conjecture of Szabó and Tardos (2006) on graph transversals asymptotically and obtain improved approximation ratios for a packet routing problem of Leighton, Maggs, and Rao (1994).
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