Sublogarithmic distributed MIS algorithm for sparse graphs using Nash-Williams decomposition

Leonid Barenboim, Michael Elkin

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

37 Scopus citations

Abstract

We study the distributed maximal independent set (henceforth, MIS) problem on sparse graphs. Currently, there are known algorithms with a sublogarithmic running time for this problem on oriented trees and graphs of bounded degrees. We devise the first sublogarithmic algorithm for computing MIS on graphs of bounded arboricity. This is a large family of graphs that includes graphs of bounded degree, planar graphs, graphs of bounded genus, graphs of bounded treewidth, graphs that exclude a fixed minor, and many other graphs. We also devise efficient algorithms for coloring graphs from these families. These results are achieved by the following technique that may be of independent interest. Our algorithm starts with computing a certain graph-theoretic structure, called Nash-Williams forests-decomposition. Then this structure is used to compute the MIS or coloring. Our results demonstrate that this methodology is very powerful. Finally, we show nearly-tight lower bounds on the running time of any distributed algorithm for computing a forests decomposition.

Original languageEnglish
Title of host publicationPODC'08
Subtitle of host publicationProceedings of the 27th Annual ACM Symposium on Principles of Distributed Computing
PublisherAssociation for Computing Machinery (ACM)
Pages25-34
Number of pages10
ISBN (Print)9781595939890
DOIs
StatePublished - 1 Jan 2008
Event27th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing - Toronto, ON, Canada
Duration: 18 Aug 200821 Aug 2008

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing

Conference

Conference27th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing
Country/TerritoryCanada
CityToronto, ON
Period18/08/0821/08/08

Keywords

  • Arboricity
  • Coloring
  • Forests decomposition
  • MIS

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