On-Line Routing in All-Optical Networks

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. Raghavan and Upfal RU94] considered the oo-line version of the problem, which was further studied in AR95, KP96, MKR95, Ra96]. For a line topology, the problem is the well-studied interval graph coloring problem. On-line algorithms for this problem have been analyzed in KT81]. We consider trees, trees of rings, and meshes topologies. previously studied in the oo-line case. We give on-line algorithms with competitive ratio O(log n) for all these topologies. We give a matching (log n) lower bound for meshes. We also prove that any algorithm for trees cannot have competitive ratio better than (log n log log n). We also consider the problem where every edge is associated with parallel links. While in WDM technology, a ber link requires diierent wavelengths for every transmission, SDM (space division multiplexing) technology allows parallel links for a single wavelength, at an additional cost. Thus, it may be beneecial in terms of network economics to combine between the two technologies (this is indeed done in practice). For arbitrary networks with (log n) parallel links we give an on-line algorithm with competitive ratio O(log n).