An Algorithmic Proof of the Lopsided Lovasz Local Lemma.

For any probability space and a collection of events with what we call a lopsided association graph, we give an algorithmic proof of the Lopsided Lovasz Local Lemma, and its stronger known forms. The only algorithmic assumption is the availability of a resampling oracle for each event. The resampling oracles act as an abstraction layer that isolates the details of the proof from the details of the probability space. The number of resamplings performed by the algorithm is bounded by expressions similar to those obtained by Moser and Tardos, and others. The overall computational efficiency depends on the runtime of the resampling oracles. We develop efficient resampling oracles for the known uses of the Lopsided Lovasz Local Lemma, unifying previous algorithmic applications and presenting new results for packings of Latin transversals, rainbow matchings and rainbow spanning trees.