Communication complexity of approximate maximum matching in the message-passing model

Huang, Zengfeng, Radunovic, Bozidar, Vojnovic, Milan ORCID: 0000-0003-1382-022X and Zhang, Qin (2020) Communication complexity of approximate maximum matching in the message-passing model. Distributed Computing, 33 (6). 515 - 531. ISSN 0178-2770

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Abstract

We consider the communication complexity of finding an approximate maximum matching in a graph in a multi-party message-passing communication model. The maximum matching problem is one of the most fundamental graph combinatorial problems, with a variety of applications. The input to the problem is a graph G that has n vertices and the set of edges partitioned over k sites, and an approximation ratio parameter α. The output is required to be a matching in G that has to be reported by one of the sites, whose size is at least factor α of the size of a maximum matching in G. We show that the communication complexity of this problem is Ω(α2kn)information bits. This bound is shown to be tight up to a log n factor, by constructing an algorithm, establishing its correctness, and an upper bound on the communication cost. The lower bound also applies to other graph combinatorial problems in the message-passing communication model, including max-flow and graph sparsification.

Item Type:	Article
Official URL:	https://www.springer.com/journal/446
Additional Information:	© 2020 Springer-Verlag GmbH Germany, part of Springer Nature
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	24 Jan 2020 13:51
Last Modified:	20 Dec 2024 00:38
URI:	http://eprints.lse.ac.uk/id/eprint/103174

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