Approximating the Max Edge-Coloring Problem

  • Nicolas Bourgeois
  • Giorgio Lucarelli
  • Ioannis Milis
  • Vangelis Th. Paschos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5874)

Abstract

We study the weighted generalization of the edge coloring problem where the goal is to minimize the sum of the weights of the heaviest edges in the color classes. In particular, we deal with the approximability of this problem on bipartite graphs and trees. We first improve the best known approximation ratios for bipartite graphs of maximum degree \({\it \Delta} \geq 7\). For trees we present a polynomial 3/2-approximation algorithm, which is the first one for any special graph class with an approximation ratio less than the known ratio of two for general graphs. Also for trees, we propose a moderately exponential approximation algorithm that improves the 3/2 ratio with running time much better than that needed for the computation of an optimal solution.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Nicolas Bourgeois
    • 1
  • Giorgio Lucarelli
    • 2
  • Ioannis Milis
    • 2
  • Vangelis Th. Paschos
    • 1
  1. 1.LAMSADEUniversité Paris-DauphineFrance
  2. 2.Dept. of InformaticsAthens University of Economics and BusinessGreece

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