We consider the problem of covering multiple submodular constraints. Given a finite ground set
Improved Massively Parallel Computation Algorithms for MIS, Matching, and Vertex Cover
We present O(log logn)round algorithms in the Massively Parallel
Computation (MPC) model, with ˜O(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 nvertex 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 Δ)round
MIS algorithm in the CONGESTEDCLIQUE model of distributed
computing, which improves on the ˜O (plog Δ)round
algorithm of Ghaffari [PODC’17].
• OurO(log logn)round (1+ε)approximate maximum matching
algorithm simplifies or improves on the following prior
work: O(log2 logn)round (1 + ε)approximation algorithm
of Czumaj et al. [STOC’18] and O(log logn)round (1 + ε)
approximation algorithm of Assadi et al. [arXiv’17].
• Our O(log logn)round (2+ε)approximate minimum vertex
cover algorithm improves on an O(log logn)round O(1)
approximation of Assadi et al. [arXiv’17].
 Publication Date:
 NSFPAR ID:
 10065947
 Journal Name:
 Proceedings of the 37th ACM Principles of Distributed Computing (PODC 2018)
 Sponsoring Org:
 National Science Foundation
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