A self-stabilizing algorithm for the minimum color sum of a graph

Authors:
Huang Sun;Brice Effantin;Hamamache Kheddouci
Affiliations:
Université de Lyon, France and Laboratory LIESP, Université Lyon 1, Villeurbanne Cedex, France;Université de Lyon, France and Laboratory LIESP, Université Lyon 1, Villeurbanne Cedex, France;Université de Lyon, France and Laboratory LIESP, Université Lyon 1, Villeurbanne Cedex, France
Venue:
ICDCN'08 Proceedings of the 9th international conference on Distributed computing and networking
Year:
2008

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Abstract

The chromatic sum of a graph G is the minimum sum of colors in a vertex coloring of G. This problem has many interests like in networks, where it models the minimization of the total charge of a network. As systems are more and more large and dynamic, distributed approaches are needed to manage them. In this paper we present a self-stabilizing algorithm to determine a minimal sum of colors for a graph. Such a coloring is determined with at most O(nΔ2) changes of colors, where Δ is the maximum degree of the graph.