A Lower Bound For The Distributed Lovasz Local Lemma
STOC '16: Symposium on Theory of Computing Cambridge MA USA June, 2016(2016)
摘要
We show that any randomised Monte Carlo distributed algorithm for the Lovasz 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 is an element of O(1), where d is the maximum degree of the dependency graph. By prior work, there are distributed algorithms for the Lovasz local lemma with a running time of O(log n) rounds in bounded-degree graphs, and the best lower bound before our work was Q(log* n) rounds [Chung et al. 2014].
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关键词
Lovasz local lemma,distributed complexity,lower bounds,locality,graph colouring,sinkless orientations
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