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arXiv · 1511.00900

A Lower Bound for the Distributed Lovász Local Lemma

Sebastian Brandt·Orr Fischer·Juho Hirvonen·Barbara Keller·Tuomo Lempiäinen·Joel Rybicki·Jukka Suomela·Jara Uitto
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Abstract

We show that any randomised Monte Carlo distributed algorithm for the Lovász local lemma requires $Ω(\log \log n)$ 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 $Ω(\log^* n)$ rounds [Chung et al. 2014].

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Sebastian Brandt, Orr Fischer, Juho Hirvonen, Barbara Keller, Tuomo Lempiäinen, Joel Rybicki, Jukka Suomela, Jara Uitto. 2015-11-03. A Lower Bound for the Distributed Lovász Local Lemma. https://arxiv.org/abs/1511.00900

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