Abstract.

In optical networks, the vast bandwidth available in an optical fibre may be utilized by splitting it into several channels, each of a different wavelength. This allows signals to be routed entirely in the optical domain. This essay studies such routings, and examines the number of different wavelengths needed for irregular networks. We find the number of wavelengths needed in large random networks, in terms of the proportion of edges present. A simple greedy routing algorithm which uses no wavelength conversion is sufficient. We give an alternative lower bound on the number of wavelengths needed, which performs poorly for large random networks, but which is more appropriate for certain existimg networks. It can sometimes be used to show that heuristically-found routings are optimal.