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Focused Stochastic Local Search and the Lovász Local Lemma

We develop tools for analyzing focused stochastic local search algorithms. These are algorithms which search a state space probabilistically by repeatedly selecting a constraint that is violated in the current state and moving to a random nearby state which, hopefully, addresses the violation without introducing many new ones. A large class of such algorithms arise from the algorithmization of the Lovász Local Lemma, a non-constructive tool for proving the existence of satisfying states. Here we give tools that provide a unified analysis of such algorithms and of many more, expressing them as instances of a general framework.