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Online Dual Edge Coloring of Paths and Trees

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Approximation and Online Algorithms (WAOA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8952))

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Abstract

We study a dual version of online edge coloring, where the goal is to color as many edges as possible using only a given number, \(k\), of available colors. All of our results are with regard to competitive analysis. For paths, we consider \(k=2\), and for trees, we consider any \(k \ge 2\). We prove that a natural greedy algorithm called First-Fit is optimal among deterministic algorithms on paths as well as trees. This is the first time that an optimal algorithm for online dual edge coloring has been identified for a class of graphs. For paths, we give a randomized algorithm, which is optimal and better than the best possible deterministic algorithm. Again, it is the first time that this has been done for a class of graphs. For trees, we also show that even randomized algorithms cannot be much better than First-Fit.

L.M. Favrholdt and J.W. Mikkelsen—Supported in part by the Villum Foundation and the Danish Council for Independent Research, Natural Sciences.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark

    Lene M. Favrholdt & Jesper W. Mikkelsen

Authors
  1. Lene M. Favrholdt
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  2. Jesper W. Mikkelsen
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Correspondence to Lene M. Favrholdt .

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Editors and Affiliations

  1. Université Pierre et Marie Curie, LIP6, Paris, France

    Evripidis Bampis

  2. EPFL-IC, Lausanne, Switzerland

    Ola Svensson

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Favrholdt, L.M., Mikkelsen, J.W. (2015). Online Dual Edge Coloring of Paths and Trees. In: Bampis, E., Svensson, O. (eds) Approximation and Online Algorithms. WAOA 2014. Lecture Notes in Computer Science(), vol 8952. Springer, Cham. https://doi.org/10.1007/978-3-319-18263-6_16

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  • DOI: https://doi.org/10.1007/978-3-319-18263-6_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18262-9

  • Online ISBN: 978-3-319-18263-6

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