M. Ghaffari, Themis Gouleakis, Slobodan Mitrovic, R. Rubinfeld
{"title":"Improved Massively Parallel Computation Algorithms for MIS, Matching, and Vertex Cover","authors":"M. Ghaffari, Themis Gouleakis, Slobodan Mitrovic, R. Rubinfeld","doi":"10.1145/3212734.3212743","DOIUrl":null,"url":null,"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].","PeriodicalId":198284,"journal":{"name":"Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2018-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"117","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3212734.3212743","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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].