Satisfying a maximum number of pre-routed requests in all-optical rings

We address the problem of maximizing the number of satisfied requests in all-optical networks that use wavelength division multiplexing. We consider the case where requests are pre-routed and formulate it as the maximum path coloring problem. We study the problem for rings and present a (2/3)-approximation algorithm. Along the way we develop a fast matching technique for a special class of bipartite graphs. By using this technique we achieve an Oðnþ m log LÞ time complexity for our approximation algorithm, where n is the number of nodes, m is the number of requests and L is the maximum load of requests on a single link. 2002 Elsevier Science B.V. All rights reserved.