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Approximation algorithms for the chromatic sum

  • Track1: Graph Algorithms
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Computing in the 90's (Great Lakes CS 1989)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 507))

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Abstract

The chromatic sum of a graph G is the smallest total among all proper colorings of G using natural numbers. It was shown that computing the chromatic sum is NP-hard. In this article we prove that a simple greedy algorithm applied to sparse graphs gives a "good" approximation of the chromatic sum. For all graphs the existence of a polynomial time algorithm that approximates the chromatic sum with a linear function error implies P = NP.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Emory University, 30322, Atlanta, GA

    Ewa Kubicka & Grzegorz Kubicki

  2. Department of Computer Science, Western Michigan University, 49008, Kalamazoo, MI

    Dionisios Kountanis

Authors
  1. Ewa Kubicka
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  2. Grzegorz Kubicki
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  3. Dionisios Kountanis
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Editor information

Naveed A. Sherwani Elise de Doncker John A. Kapenga

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© 1991 Springer-Verlag Berlin Heidelberg

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Kubicka, E., Kubicki, G., Kountanis, D. (1991). Approximation algorithms for the chromatic sum. In: Sherwani, N.A., de Doncker, E., Kapenga, J.A. (eds) Computing in the 90's. Great Lakes CS 1989. Lecture Notes in Computer Science, vol 507. Springer, New York, NY. https://doi.org/10.1007/BFb0038467

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  • DOI: https://doi.org/10.1007/BFb0038467

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-97628-0

  • Online ISBN: 978-0-387-34815-5

  • eBook Packages: Springer Book Archive

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