S. Brandt, O. Fischer, J. Hirvonen, Barbara Keller, Tuomo Lempiäinen, J. Rybicki, J. Suomela, Jara Uitto
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引用次数: 112
摘要
我们证明了任何用于Lovász局部引理的随机蒙特卡罗分布式算法都需要Omega(log log n)轮通信，假设它以高概率找到正确的分配。我们的结果即使在d = O(1)的特殊情况下也成立，其中d是依赖图的最大程度。根据之前的工作，Lovász局部引理的分布式算法在有界度图中运行时间为O(log n)轮，在我们的工作之前，最好的下界是Omega(log* n)轮[Chung et al. 2014]。
A lower bound for the distributed Lovász local lemma
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].
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