Affiliation:
1. Khoury College of Computer Sciences, Northeastern University, USA
2. Department of Computer Science, University of Maryland, USA
Abstract
The study of approximate matching in the
Massively Parallel Computations
(MPC) model has recently seen a burst of breakthroughs. Despite this progress, we still have a limited understanding of
maximal matching
which is one of the central problems of parallel and distributed computing. All known MPC algorithms for maximal matching either take polylogarithmic time which is considered inefficient, or require a strictly super-linear space of
n
1+Ω (1)
per machine.
In this work, we close this gap by providing a novel analysis of an extremely simple algorithm, which is a variant of an algorithm conjectured to work by Czumaj, Lacki, Madry, Mitrovic, Onak, and Sankowski [
15
]. The algorithm edge-samples the graph, randomly partitions the vertices, and finds a random greedy maximal matching within each partition. We show that this algorithm drastically reduces the vertex degrees. This, among other results, leads to an
O
(log log Δ) round algorithm for maximal matching with
O(n)
space (or even
mildly sublinear
in
n
using standard techniques).
As an immediate corollary, we get a 2 approximate
minimum vertex cover
in essentially the same rounds and space, which is the optimal approximation factor under standard assumptions. We also get an improved
O
(log log Δ) round algorithm for 1 + ε approximate matching. All these results can also be implemented in the
congested clique
model in the same number of rounds.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
1 articles.
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