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

Author

Listed:
  • Huang, Zengfeng
  • Radunovic, Bozidar
  • Vojnovic, Milan
  • Zhang, Qin

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.

Suggested Citation

  • Huang, Zengfeng & Radunovic, Bozidar & Vojnovic, Milan & Zhang, Qin, 2020. "Communication complexity of approximate maximum matching in the message-passing model," LSE Research Online Documents on Economics 103174, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:103174
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    File URL: http://eprints.lse.ac.uk/103174/
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    More about this item

    Keywords

    approximate maximum matching; multi- party communication complexity; message passing;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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