In all-optical networks that use WDM technology it is often the case that several communication requests have to be blocked, due to bandwidth and technology limitations. Minimizing request blocking is therefore an important task calling for algorithmic techniques for efficient routing and wavelength assignment. Here we study the problem for rings under both the undirected and the directed settings, corresponding to symmetric and one-way communication respectively. The problem in graph-theoretic terms can be formulated as the Maximum Routing and Path Coloring Problem. We present a Chain-and-Matching technique for routing requests and coloring the corresponding paths which gives constant approximations for both the undirected and the directed cases. For the undirected problem we obtain a 2/3-approximation algorithm; this corresponds to a considerable increase in the number of satisfied requests compared to the best known algorithm so far, due to Wan and Liu [1], that achieves a 1 - 1/e ratio using iteratively a maximum edge-disjoint paths algorithm. For the directed case, we also introduce a Balanced Matching method which, combined with the Chain-and-Matching technique, gives a 7/11-approximation algorithm. This algorithm also improves upon the (1 - 1/e)-approximation algorithm that can be obtained by extending the iterative method of [1].
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