Weighted coloring: further complexity and approximability results

Authors:
Bruno Escoffier;Jérôme Monnot;Vangelis Th. Paschos
Affiliations:
LAMSADE, CNRS and Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, Paris Cedex, France;LAMSADE, CNRS and Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, Paris Cedex, France;LAMSADE, CNRS and Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, Paris Cedex, France
Venue:
Information Processing Letters
Year:
2006

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Abstract

Given a vertex-weighted graph G = (V, E; w), w(v) ≥ 0 for any v ∈ V, we consider a weighted version of the coloring problem which consists in finding a partition S = (S1..., Sk) of the vertex set of G into stable sets and minimizing Σi=1k w(Si) where the weight of S is defined as max{w(v): v ∈ S}. In this paper, we continue the investigation of the complexity and the approximability of this problem by answering some of the questions raised by Guan and Zhu [D.J. Guan, X. Zhu, A coloring problem for weighted graphs, Inform. Process. Lett. 61 (2) (1997) 77-81].