Improved Massively Parallel Computation Algorithms for MIS, Matching, and Vertex Cover

M. Ghaffari, Themis Gouleakis, Slobodan Mitrovic, R. Rubinfeld
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引用次数: 117

Abstract

We present O(loglog n) -round algorithms in the Massively Parallel Computation (MPC) model, with Õ (n) memory per machine, that compute a maximal independent set, a 1+ε approximation of maximum matching, and a 2+εapproximation of minimum vertex cover, for any n-vertex graph and any constant \eps>0. These improve the state of the art as follows: Our MIS algorithm leads to a simple O(loglog Δ)-round MIS algorithm in the CONGESTED-CLIQUE model of distributed computing, which improves on the Õ (√log Δ )-round algorithm of Ghaffari [PODC'17]. Our O(loglog n)-round (1+ε)-approximate maximum matching algorithm simplifies or improves on the following prior work: O(log^2log n)-round (1+\eps)-approximation algorithm of Czumaj et al. [STOC'18] and $O(loglog n)-round (1+ε)-approximation algorithm of Assadi et al. [arXiv'17]. Our O(loglog n)-round (2+ε)-approximate minimum vertex cover algorithm improves on an O(loglog n)-round O(1)-approximation of Assadi et al. [arXiv'17].
改进的MIS,匹配和顶点覆盖的大规模并行计算算法
我们提出了大规模并行计算(MPC)模型中的O(loglog n)轮算法,每台机器具有Õ (n)内存,对于任何n顶点图和任何常数\eps>0,该算法计算最大独立集,最大匹配的1+ε近似和最小顶点覆盖的2+ε近似。这些改进了目前的技术水平如下:我们的MIS算法在分布式计算的congeded - clique模型中产生了一个简单的O(log Δ)轮MIS算法,它改进了Ghaffari [PODC'17]的Õ(√log Δ)轮算法。我们的O(loglog n)-round (1+ε)-近似最大匹配算法简化或改进了以下先前的工作:Czumaj等人的O(log^2log n)-round (1+\eps)-近似算法[STOC'18]和Assadi等人的O(loglog n)-round (1+ε)-近似算法[arXiv'17]。我们的O(loglog n)-round (2+ε)-近似最小顶点覆盖算法改进了Assadi等人的O(loglog n)-round O(1)-近似[arXiv'17]。
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