On shortest-path all-optical networks without wavelength conversion requirements

Abstract

In all-optical networks with wavelength-division multiplexing, every connection is routed along a certain path and assigned a wavelength such that no two connections use the same wavelength on the same link. For a given set P of paths (a routing), let χ(P) denote the minimum number of wavelengths in a valid wavelength assignment and let L(P) denote the maximum link load. We always have L(P)/<-χ(P). Motivated by practical concerns, we consider routings containing only shortest paths. We give a complete characterization of undirected networks for which any set P of shortest paths admits a wavelength assignment with L(P) wavelengths. These are exactly the networks that do not benefit from the use of (expensive) wavelength converters if shortest-path routing is used.We also give an efficient algorithm for computing awavelength assignment with L(P) wavelengths in these networks.