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Online Dual Edge Coloring of Paths and Trees

  • Lene M. Favrholdt
  • Jesper W. Mikkelsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8952)

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.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of Southern DenmarkOdenseDenmark

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