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On the max-weight edge coloring problem

Author

Listed:
  • Giorgio Lucarelli

    (Athens University of Economics and Business)

  • Ioannis Milis

    (Athens University of Economics and Business)

  • Vangelis T. Paschos

    (LAMSADE, CNRS UMR 7024 and Université Paris-Dauphine)

Abstract

We study the following generalization of the classical edge coloring problem: Given a weighted graph, find a partition of its edges into matchings (colors), each one of weight equal to the maximum weight of its edges, so that the total weight of the partition is minimized. We explore the frontier between polynomial and NP-hard variants of the problem, with respect to the class of the underlying graph, as well as the approximability of NP-hard variants. In particular, we present polynomial algorithms for bounded degree trees and star of chains, as well as an approximation algorithm for bipartite graphs of maximum degree at most twelve which beats the best known approximation ratios.

Suggested Citation

  • Giorgio Lucarelli & Ioannis Milis & Vangelis T. Paschos, 2010. "On the max-weight edge coloring problem," Journal of Combinatorial Optimization, Springer, vol. 20(4), pages 429-442, November.
    • Handle: RePEc:spr:jcomop:v:20:y:2010:i:4:d:10.1007_s10878-009-9223-z
    DOI: 10.1007/s10878-009-9223-z
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    References listed on IDEAS

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    1. Foto Afrati & Timos Aslanidis & Evripidis Bampis & Ioannis Milis, 2005. "Scheduling in Switching Networks with Set-Up Delays," Journal of Combinatorial Optimization, Springer, vol. 9(1), pages 49-57, February.
    2. Pierluigi Crescenzi & Xiaotie Deng & Christos H. Papadimitriou, 2001. "On Approximating a Scheduling Problem," Journal of Combinatorial Optimization, Springer, vol. 5(3), pages 287-297, September.
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    1. Foto Afrati & Timos Aslanidis & Evripidis Bampis & Ioannis Milis, 2005. "Scheduling in Switching Networks with Set-Up Delays," Journal of Combinatorial Optimization, Springer, vol. 9(1), pages 49-57, February.

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