Distance-2 Self-stabilizing Algorithm for a b-Coloring of Graphs

Authors:
Lyes Dekar;Hamamache Kheddouci
Affiliations:
Lab. LIESP, Université Lyon 1, IUTA, Département Informatique, Université de Lyon, Bourg en Bresse, France F-01000;Laboratoire LIESP, Université Lyon 1, Université de Lyon, Villeurbanne Cedex, France 69622
Venue:
SSS '08 Proceedings of the 10th International Symposium on Stabilization, Safety, and Security of Distributed Systems
Year:
2008

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Abstract

A b-coloring of a graph G is a proper k -coloring of Gsuch that for each color i , 1 ≤ i ≤k , at least one vertex colored with i is adjacentto every color j , with 1 ≤ j ≠ i ≤ k . This kind of coloring is useful to decompose anysystem into communities, where each community contains a vertexadjacent to all the other communities. This kind of organizationcan provide improving in many fields, especially in the dataclustering. In this paper we propose a new self-stabilizingalgorithm for finding a b-coloring of arbitrary undirectedconnected graphs. Because the characteristics of the b-coloringproblem, the proposed self-stabilizing algorithm use a distance-2knowledge.