TY - GEN

T1 - Improved massively parallel computation algorithms for MIS, matching, and vertex cover

AU - Ghaffari, Mohsen

AU - Gouleakis, Themis

AU - Konrad, Christian

AU - Mitrović, Slobodan

AU - Rubinfeld, Ronitt

N1 - Publisher Copyright:
© 2018 Association for Computing Machinery.

PY - 2018/7/23

Y1 - 2018/7/23

N2 - 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 + approximation of maximum matching, and a 2 + approximation of minimum vertex cover, for any n-vertex graph and any constant > 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+)-approximate maximum matching algorithm simplifies or improves on the following prior work: O(log2 log n)-round (1 +)-approximation algorithm of Czumaj et al. [STOC'18] and O(log log n)-round (1 + )- approximation algorithm of Assadi et al. [arXiv'17]. • Our O(log log n)-round (2 +)-approximate minimum vertex cover algorithm improves on an O(log log n)-round O(1)approximation of Assadi et al. [arXiv'17].

AB - 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 + approximation of maximum matching, and a 2 + approximation of minimum vertex cover, for any n-vertex graph and any constant > 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+)-approximate maximum matching algorithm simplifies or improves on the following prior work: O(log2 log n)-round (1 +)-approximation algorithm of Czumaj et al. [STOC'18] and O(log log n)-round (1 + )- approximation algorithm of Assadi et al. [arXiv'17]. • Our O(log log n)-round (2 +)-approximate minimum vertex cover algorithm improves on an O(log log n)-round O(1)approximation of Assadi et al. [arXiv'17].

KW - Congested clique

KW - Massively parallel computation

KW - Maximal independent set

KW - Maximum matching

KW - Vertex cover

UR - http://www.scopus.com/inward/record.url?scp=85052471321&partnerID=8YFLogxK

U2 - 10.1145/3212734.3212743

DO - 10.1145/3212734.3212743

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AN - SCOPUS:85052471321

SN - 9781450357951

T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

SP - 129

EP - 138

BT - PODC 2018 - Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing

PB - Association for Computing Machinery

T2 - 37th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2018

Y2 - 23 July 2018 through 27 July 2018

ER -