TY - GEN

T1 - Sublogarithmic distributed MIS algorithm for sparse graphs using Nash-Williams decomposition

AU - Barenboim, Leonid

AU - Elkin, Michael

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

KW - Arboricity

KW - Coloring

KW - Forests decomposition

KW - MIS

UR - http://www.scopus.com/inward/record.url?scp=57549110840&partnerID=8YFLogxK

U2 - 10.1145/1400751.1400757

DO - 10.1145/1400751.1400757

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AN - SCOPUS:57549110840

SN - 9781595939890

T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

SP - 25

EP - 34

BT - PODC'08

PB - Association for Computing Machinery (ACM)

T2 - 27th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing

Y2 - 18 August 2008 through 21 August 2008

ER -