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Approximation algorithms for the chromatic sum

  • Ewa Kubicka
  • Grzegorz Kubicki
  • Dionisios Kountanis
Track1: Graph Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 507)

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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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Ewa Kubicka
    • 1
  • Grzegorz Kubicki
    • 1
  • Dionisios Kountanis
    • 2
  1. 1.Department of Mathematics and Computer ScienceEmory UniversityAtlanta
  2. 2.Department of Computer ScienceWestern Michigan UniversityKalamazoo

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