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

We investigate a variant of on-line edge-coloring in which there is a fixed number of colors availableandtheaimistocolorasmanyedgesaspossible.Weproveupperandlowerboundsontheperformance 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 lon...

• Type: Conference
• Year: 2000
• Where: FSTTCS
• Authors: Lene M. Favrholdt, Morten N. Nielsen
• Keywords: Competitive Ratio, Fair Algorithms, Fixed Number, FSTTCS 2000, Software Engineering