NDLI: Sublogarithmic distributed MIS algorithm for sparse graphs using nash-williams decomposition

Content Provider	ACM Digital Library
Author	Barenboim, Leonid Elkin, Michael
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.
Starting Page	25
Ending Page	34
Page Count	10
File Format	PDF
ISBN	9781595939890
DOI	10.1145/1400751.1400757
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2008-08-18
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Coloring Arboricity Mis Forests decomposition
Content Type	Text
Resource Type	Article

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Sublogarithmic distributed MIS algorithm for sparse graphs using nash-williams decomposition