Improved Massively Parallel Computation Algorithms for MIS, Matching, and Vertex Cover
Name
1802.08237.pdf
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Accepted version
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362.2 KB
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Author(s)
Ghaffari, Mohsen
Gouleakis, Themistoklis
Konrad, Christian
Mitrović, Slobodan
Rubinfeld, Ronitt
Date Issued
July 2018
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
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].
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
https://doi.org/10.1145/3212734.3212743
