Wavelength Conversion in Optical Networks
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In many models of optical routing, we are given a set of communication paths in a network, and we must assign a wavelength to each path so that paths sharing an edge receive different wavelengths. The goal is to assign as few wavelengths as possible, in order to make as efficient use as possible of the optical bandwidth. Wilfong and Winkler considered the problem of placing wavelength converters in such a network: if a node of the network contains a converter, any path that passes through this node may change its wavelength. Having converters at some of the nodes can reduce the number of wavelengths required for routing, down to the following natural {\em congestion bound}: even with converters, we will always need at least as many wavelengths as the maximum number of paths sharing a single edge. Thus Winkler and Wilfong defined a set