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

Author(s)
Ghaffari, Mohsen; Gouleakis, Themistoklis; Konrad, Christian; Mitrović, Slobodan; Rubinfeld, Ronitt
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Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/
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Abstract
We present O(log log 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 + ε approximation of minimum vertex cover, for any n-vertex graph and any constant ε > 0. These improve the state of the art as follows: • Our MIS algorithm leads to a simple O(log log ∆)-round MIS algorithm in the CONGESTED-CLIQUE model of distributed computing, which improves on the Õ(log ∆)-round algorithm of Ghaffari [PODC'17]. • Our O(log log n)-round (1+ ε)-approximate maximum matching algorithm simplifies or improves on the following prior work: O(log² log n)-round (1 + ε)-approximation algorithm of Czumaj et al. [STOC'18] and O(log log n)-round (1 + ε)- approximation algorithm of Assadi et al. [SODA'19]. • Our O(log log n)-round (2 + ε)-approximate minimum vertex cover algorithm improves on an O(log log n)-round O(1)approximation of Assadi et al. [arXiv'17].
Date issued
2018-07
URI
https://hdl.handle.net/1721.1/129790
Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Journal
PODC '18: Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing
Publisher
ACM
Citation
Ghaffari, Mohsen et al. "Improved Massively Parallel Computation Algorithms for MIS, Matching, and Vertex Cover." PODC '18: Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing, July 2018, Egham, United Kingdom, Association for Computing Machinery, New York, NY, United States, 129–138. © 2018 Association for Computing Machinery.
Version: Author's final manuscript
ISBN
9781450357951

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