A lower bound for the distributed Lovász local lemma

Sebastian Brandt, Orr Fischer, Juho Hirvonen, Barbara Keller, Tuomo Lempiäinen, Joel Rybicki, Jukka Suomela and Jara Uitto.

STOC 2016



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].