Local 7-coloring for planar subgraphs of unit disk graphs

Authors:
J. Czyzowicz;S. Dobrev;H. González-Aguilar;R. Kralovic;E. Kranakis;J. Opatrny;L. Stacho;J. Urrutia
Affiliations:
Département dinformatique, Université du Québec en Outaouais, Gatineau, Québec J8X 3X7, Canada;Slovak Academy of Sciences, Bratislava, Slovakia;Centro de Investigacion en Matematicas, Guanajuato, Gto., C.P. 36000, Mexico;Department of Computer Science, Faculty of Mathematics, Physics and Informatics Comenius University, Bratislava, Slovakia;School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, Canada, K1S 5B6;Department of Computer Science, Concordia University, 1455 de Maisonneuve Blvd West, Montréal, Quebec, Canada, H3G 1M8;Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia, Canada, V5A 1S6;Instituto de Matemáticas, Universidad Nacional Autónoma de México, Área de la investigación cientifica, Circuito Exterior, Ciudad Universitaria, Coyoacán 04510, M ...
Venue:
Theoretical Computer Science
Year:
2011

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Abstract

We study the problem of computing locally a coloring of an arbitrary planar subgraph of a unit disk graph. Each vertex knows its coordinates in the plane and can communicate directly with all its neighbors within unit distance. Using this setting, first a simple algorithm is given whereby each vertex can compute its color in a 9-coloring of the planar graph using only information on the subgraph located within at most 9 hops away from it in the original unit disk graph. A more complicated algorithm is then presented whereby each vertex can compute its color in a 7-coloring of the planar graph using only information on the subgraph located within a constant number (201, to be exact) of hops away from it.