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

  • Lyes Dekar
  • Hamamache Kheddouci
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5340)


A b-coloring of a graph G is a proper k-coloring of G such that for each color i, 1 ≤ i ≤ k, at least one vertex colored with i is adjacent to every color j, with 1 ≤ j ≠ i ≤ k. This kind of coloring is useful to decompose any system into communities, where each community contains a vertex adjacent to all the other communities. This kind of organization can provide improving in many fields, especially in the data clustering. In this paper we propose a new self-stabilizing algorithm for finding a b-coloring of arbitrary undirected connected graphs. Because the characteristics of the b-coloring problem, the proposed self-stabilizing algorithm use a distance-2 knowledge.


b-coloring self-stabilizing algorithm clustering data mining graphs 


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© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Lyes Dekar
    • 1
  • Hamamache Kheddouci
    • 2
  1. 1.Lab. LIESP, Université Lyon 1, IUTA, Département InformatiqueUniversité de LyonBourg en BresseFrance
  2. 2.Laboratoire LIESP, Université Lyon 1Université de LyonVilleurbanne CedexFrance

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