Distributed maximum matching in bounded degree graphs

Guy Even, Moti Medina, Dana Ron

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We present deterministic distributed algorithms for computing approximate maximum cardinality matchings and approximate maximum weight matchings. Our algorithm for the unweighted case computes a matching whose size is at least (1 - ε) times the optimal in ΔO(1/ε) + O (1/ε2)·log∗(n) rounds where n is the number of vertices in the graph and Δ is the maximum degree. Our algorithm for the edge-weighted case computes a matching whose weight is at least (1 - ε) times the optimal in log(min{1/wmin, n/ε})O(1/ε)·(ΔO(1/ε) + log∗(n)) rounds for edge-weights in [wmin, 1]. The best previous algorithms for both the unweighted case and the weighted case are by Lotker, Patt-Shamir, and Pettie (SPAA 2008). For the unweighted case they give a randomized (1 - ε)-approximation algorithm that runs in O((log(n))/ε3) rounds. For the weighted case they give a randomized (1/2 - ε)-approximation algorithm that runs in O(log(ε-1)·log(n)) rounds. Hence, our results improve on the previous ones when the parameters Δ, ε and wmin are constants (where we reduce the number of runs from O(log(n)) to O(log∗(n))), and more generally when Δ, 1/ε and 1/wmin are sufficiently slowly increasing functions of n. Moreover, our algorithms are deterministic rather than randomized.

Original languageEnglish
Title of host publicationICDCN 2015 - Proceedings of the 16th International Conference on Distributed Computing and Networking
PublisherAssociation for Computing Machinery
ISBN (Electronic)9781450329286
DOIs
StatePublished - 4 Jan 2015
Event16th International Conference on Distributed Computing and Networking, ICDCN 2015 - Goa, India
Duration: 4 Jan 20157 Jan 2015

Publication series

NameACM International Conference Proceeding Series
Volume04-07-January-2015

Conference

Conference16th International Conference on Distributed Computing and Networking, ICDCN 2015
Country/TerritoryIndia
CityGoa
Period4/01/157/01/15

Keywords

  • Centralized local algorithms
  • Distributed local algorithms
  • Graph algorithms
  • Maximum matching
  • Maximum weighted matching

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