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A 27/26-Approximation Algorithm for the Chromatic Sum Coloring of Bipartite Graphs

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Book cover Approximation Algorithms for Combinatorial Optimization (APPROX 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2462))

Abstract

We consider the Chromatic Sum Problem on bipartite graphs which appears to be much harder than the classical Chromatic Number Problem. We prove that the Crmatic Sum Problem is NP-complete on planar bipartite graphs with ∇≤ 5, but polynomial on bipartite graphs with ∇≤ 3, for which we construct an O(n 2)-time algorithm. Hence, we tighten the borderline of intractability for this problem on bipartite graphs with bounded degree, namely: the case ∇ = 3 is easy, ∇ = 5 is hard. Moreover, we construct a 27/26-approximation algorithm for this problem thus improving the best known approximation ratio of 10/9.

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Author information

Authors and Affiliations

  1. Foundations of Informatics Department, Gdańsk University of Technology, Poland

    Krzysztof Giaro, Robert Janczewski, Marek Kubale & Michał Małafiejski

Authors
  1. Krzysztof Giaro
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  2. Robert Janczewski
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  3. Marek Kubale
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  4. Michał Małafiejski
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Editor information

Editors and Affiliations

  1. Institut für Informatik und praktische Mathematik, Universität Kiel, Olshausenstr. 40, 24098, Kiel, Germany

    Klaus Jansen

  2. Dipartimento di Informatika e Sistemistica, Universita di Roma La Sapienza, Via Salaria 113, 00198, Roma, Italy

    Stefano Leonardi

  3. College of Computing, Georgia Institute of Technology, 801 Atlantic Drive, Atlanta, 30332-0280, Georgia, USA

    Vijay Vazirani

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© 2002 Springer-Verlag Berlin Heidelberg

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Giaro, K., Janczewski, R., Kubale, M., Małafiejski, M. (2002). A 27/26-Approximation Algorithm for the Chromatic Sum Coloring of Bipartite Graphs. In: Jansen, K., Leonardi, S., Vazirani, V. (eds) Approximation Algorithms for Combinatorial Optimization. APPROX 2002. Lecture Notes in Computer Science, vol 2462. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45753-4_13

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  • DOI: https://doi.org/10.1007/3-540-45753-4_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44186-1

  • Online ISBN: 978-3-540-45753-4

  • eBook Packages: Springer Book Archive

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