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 d'informatique, Université du Québec en Outaouais, Gatineau, Québec, Canada;Slovak Academy of Sciences, Bratislava, Slovakia;Centro de Investigacion en Matematicas, Guanajuato, Gto., Mexico;Department of Computer Science, Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia;School of Computer Science, Carleton University, Ottawa, Ontario, Canada;Department of Computer Science, Concordia University, Montréal, Qubec, Canada;Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada;Instituto de Matemáticas, Universidad Nacional Autónoma de México, México, D.F. México

  • Venue:
  • TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
  • Year:
  • 2008

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Abstract

The problem of computing locally a coloring of an arbitrary planar subgraph of a unit disk graph is studied. Each vertex knows its coordinates in the plane, can directly communicate 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 of hops away from it.