Focused Stochastic Local Search and the Lov\'asz Local Lemma

TL;DR

This paper introduces a unified analytical framework for focused stochastic local search algorithms, especially those derived from the Lovász Local Lemma, enhancing understanding of their probabilistic behavior.

Contribution

It develops new tools for analyzing focused stochastic local search algorithms, unifying their analysis and extending applicability beyond existing methods.

Findings

Provides a general framework for analyzing these algorithms

Unifies analysis of Lovász Local Lemma-based algorithms

Extends understanding of probabilistic local search methods

Abstract

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 Lov\'asz 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.