Competitive Online Graph Edge Coloring Algorithm

A natural question then is how well we can do A classic theorem by Vizing proves that if the maximum in the online setting, where the edges of the graph are degree of a graph is Δ, then it is possible to color its edges, revealed one by one, and we need to color each edge as in polynomial time, using at most Δ+1 colors. However, this soon as it is

added to the graph. algorithm is offline, i.e., it assumes the whole graph is known Fast online edge coloring algorithms are not just of in advance. A natural question then is how well we can do in theoretical interest, but also important in high speed the online setting, where the edges of the graph are revealed network switching. Bipartite edge coloring has a direct one by one, and we need to color each edge as soon as it is application in switch scheduling, see [1] and the refer- added to the graph. Online edge coloring has an important ences there for details. A natural model here is that the application in fast switch scheduling. Here, a natural model edges arrive online in a random permutation. This is is that edges arrive online, but in a random permutation. the input model we work with in this paper. We will Even in the random permutations model, the best analysis restrict our attention to bipartite graphs: this is with- for any algorithm is factor 2, which comes from the simple out loss of generality (see an explanation in [9] for the greedy algorithm (which is factor 2 even in the worst case reduction...

Website: www.siam.org | Filesize: -
No of Page(s): 9
Download A 1.43-Competitive Online Graph Edge Coloring Algorithm In ... - SIAM.pdf