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The Probabilistic Minimum Coloring Problem

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Graph-Theoretic Concepts in Computer Science (WG 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2880))

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Abstract

We study the probabilistic coloring problem (pcolor) under a modification strategy consisting, given an a priori solution C, of removing the absent vertices from C. We compute the objective function associated with this strategy, we give bounds on its value, we characterize the complexity of computing it and the one of computing the optimal solution associated with. We show that pcolor is NP-hard and design a polynomial time approximation algorithm achieving non-trivial approximation ratio. We then show that probabilistic coloring remains NP-hard even in bipartite graphs and that the unique 2-coloring in such graphs is a constant ratio approximation. We finally prove that pcolor is polynomial when dealing with complements of bipartite graphs.

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Author information

Authors and Affiliations

  1. LAMSADE, Université Paris-Dauphine, Place du Maréchal De Lattre de Tassigny, 75775, Paris Cedex 16, France

    Cécile Murat & Vangelis Th. Paschos

Authors
  1. Cécile Murat
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  2. Vangelis Th. Paschos
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Editor information

Editors and Affiliations

  1. Department of Information and Computing Sciences, Utrecht University, The Netherlands

    Hans L. Bodlaender

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© 2003 Springer-Verlag Berlin Heidelberg

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Murat, C., Paschos, V.T. (2003). The Probabilistic Minimum Coloring Problem. In: Bodlaender, H.L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2003. Lecture Notes in Computer Science, vol 2880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39890-5_30

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  • DOI: https://doi.org/10.1007/978-3-540-39890-5_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20452-7

  • Online ISBN: 978-3-540-39890-5

  • eBook Packages: Springer Book Archive

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