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Algorithmica

, Volume 35, Issue 2, pp 176–191 | Cite as

On-Line Edge-Coloring with a Fixed Number of Colors

  • Monrad Favrholdt
  • Nyhave  Nielsen
Article

Abstract

We investigate a variant of on-line edge-coloring in which there is a fixed number of colors available and the aim is to color as many edges as possible. We prove upper and lower bounds on the performance of different classes of algorithms for the problem. Moreover, we determine the performance of two specific algorithms, First-Fit and Next-Fit .

Specifically, algorithms that never reject edges that they are able to color are called fair algorithms. We consider the four combinations of fair/ not fair and deterministic/ randomized.

We show that the competitive ratio of deterministic fair algorithms can vary only between approximately 0.4641 and 1/2, and that Next-Fit is worst possible among fair algorithms. Moreover, we show that no algorithm is better than 4/7-competitive.

If the graphs are all k -colorable, any fair algorithm is at least 1/2-competitive. Again, this performance is matched by Next-Fit while the competitive ratio for First-Fit is shown to be k/(2k-1) , which is significantly better, as long as k is not too large.

Keywords

Edge-coloring On-line algorithms Competitive analysis Fixed number of colors Maximization problem Fair algorithms k -Colorable graphs Accommodating sequences Restricted adversary Randomization 

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Copyright information

© Springer-Verlag New York Inc. 2002

Authors and Affiliations

  • Monrad Favrholdt
    • 1
  • Nyhave  Nielsen
    • 1
  1. 1.Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, lenem@imada.sdu.dk, nyhave@imada.sdu.dk.Denmark

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