An Algorithmic Proof of the Lopsided Lovász Local Lemma (simplified and condensed into lecture notes)

For any probability space and a collection of events we give an algorithmic proof of the Lovász Local Lemma if there is 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 that unify previous algorithmic applications of the local lemma, and present new results for rainbow matchings. The long version of this paper is available at http://arxiv.org/abs/1504.02044