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

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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 an 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.

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Authors and Affiliations

  1. Department of Computer Science, Ben-Gurion University of the Negev, P.O. Box 653, 84105, Beer-Sheva, Israel

    Leonid Barenboim & Michael Elkin

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  1. Leonid Barenboim
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  2. Michael Elkin
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Correspondence to Leonid Barenboim.

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This research has been supported by the Israeli Academy of Science, grant 483/06.

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Barenboim, L., Elkin, M. Sublogarithmic distributed MIS algorithm for sparse graphs using Nash-Williams decomposition. Distrib. Comput. 22, 363–379 (2010). https://doi.org/10.1007/s00446-009-0088-2

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  • DOI: https://doi.org/10.1007/s00446-009-0088-2

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