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.

Research partially supported by the Swiss National Science Foundation under Contract No. 21- 63563.00 (Project AAPCN) and the EU Thematic Network APPOL II (IST-2001-32007), with funding provided by the Swiss Federal Office for Education and Science (BBW).