A Lower Bound for the Distributed Lovász Local Lemma

Abstract

We show that any randomised Monte Carlo distributed algorithm for the Lovász local lemma requires Omega(log log n) communication rounds, assuming that it finds a correct assignment with high probability. Our result holds even in the special case of d = O(1), where d is the maximum degree of the dependency graph. By prior work, there are distributed algorithms for the Lovász local lemma with a running time of O(log n) rounds in bounded-degree graphs, and the best lower bound before our work was Omega(log* n) rounds [Chung et al. 2014].

DOI: 10.1145/2897518.2897570

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Cite this paper

@inproceedings{Brandt2016ALB, title={A Lower Bound for the Distributed Lov{\'a}sz Local Lemma}, author={Sebastian Brandt and Orr Fischer and Juho Hirvonen and Barbara Keller and Tuomo Lempi{\"a}inen and Joel Rybicki and Jukka Suomela and Jara Uitto}, booktitle={STOC}, year={2016} }