The paper deals with on-line routing in WDM(wavelength division multiplexing) optical networks. A sequence of requests arrives over time, each is a pair of nodes to be connected by a path. The problem is to assign a wavelength and a path to each pair,so that no two paths sharing a link are assigned the same wavelength. The goal is to minimize the number of wavelengths used to establish all connections. We consider trees, trees of rings, and meshes topologies. We give on-line algorithms with competitive ratio O(log n) for all these topologies. We give a matching #OMEGA#(log n) lower bound for meshes. We also prove that any algorithm for trees cannot have competitive ratio better than #OMEGA#(log n/log log n). We also consider the problem where every edge is associated with parallel links. While in WDM technology, a fiber link requires different wavelengths for every transmission, SDM (space division multiplexing) technology allows parallel links for a single wavelength, at an additional cost. Thus, it may be beneficial in terms of network economics to combine between the two technologies (this is indeed done in practice). For arbitrary networks with #OMEGA#(log n) parallel links we give an on-line algorithm with competitive ratio O(log n).
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