Comparing First-Fit and Next-Fit for Online Edge Coloring

  • Martin R. Ehmsen
  • Lene M. Favrholdt
  • Jens S. Kohrt
  • Rodica Mihai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5369)


We study the performance of the algorithms First-Fit and Next-Fit for two online edge coloring problems. In the min-coloring problem, all edges must be colored using as few colors as possible. In the max-coloring problem, a fixed number of colors is given, and as many edges as possible should be colored. Previous analysis using the competitive ratio has not separated the performance of First-Fit and Next-Fit, but intuition suggests that First-Fit should be better than Next-Fit. We compare First-Fit and Next-Fit using the relative worst order ratio, and show that First-Fit is better than Next-Fit for the min-coloring problem. For the max-coloring problem, we show that First-Fit and Next-Fit are not strictly comparable, i.e., there are graphs for which First-Fit is better than Next-Fit and graphs where Next-Fit is slightly better than First-Fit.


Competitive Ratio Online Algorithm Complete Bipartite Graph Expander Graph Majority Coloring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Martin R. Ehmsen
    • 1
  • Lene M. Favrholdt
    • 1
  • Jens S. Kohrt
    • 1
  • Rodica Mihai
    • 2
  1. 1.Department of Mathematics and Computer ScienceUniversity of Southern DenmarkDenmark
  2. 2.Department of InformaticsUniversity of BergenNorway

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