An incremental distributed algorithm for a partial Grundy coloring of graphs

  • Authors:

  • Lyes Dekar;Brice Effantin;Hamamache Kheddouci

  • Affiliations:

  • Université de Lyon, Lyon, France and Laboratoire LIESP, Université Lyon1, IUTA, Département Informatique, Bourg en Bresse, France;Université de Lyon, Lyon, France and Laboratoire LIESP, Université Lyon1, Villeurbanne Cedex, France;Université de Lyon, Lyon, France and Laboratoire LIESP, Université Lyon1, Villeurbanne Cedex, France

  • Venue:
  • ISPA'07 Proceedings of the 5th international conference on Parallel and Distributed Processing and Applications
  • Year:
  • 2007

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Abstract

A coloring of a graph G=(V,E) is a partition of {V1,V2...Vk} of V into k independent sets called color classes. A vertex v∈Vi is called a Grundy vertex if it is adjacent to at least one vertex in color class Vj, for every j . In the partial Grundy coloring, every color class contains at least one Grundy vertex. Such a coloring gives a partitioning of the graph into clusters for which every cluster has a clusterhead (the Grundy vertex) adjacent to some other clusters. Such a decomposition is very interesting for large distributed systems and networks. In this paper, we propose a distributed algorithm to maintain the partial Grundy coloring of any graph G when an edge is added