All-to-all wavelength-routing in all-optical compound networks Original Research Article

We give theoretical results obtained for wavelength routings in certain all-optical networks. In all-optical networks a single physical optical link can carry several logical signals provided that they are transmitted on different wavelengths. An all-to-all routing in a n-node network is a set of n(n−1) simple paths specified for every ordered pair (x,y) of nodes. The routing will be feasible if an assignment of wavelengths to the paths can be given such that no link will carry in the same direction two different paths of the routing on the same wavelength. With such a routing, it is possible to perform the gossiping in one round. The cost of the routing depends on the number of wavelengths it handles. We give the smallest necessary number of wavelength over all possible routings for networks based on certain compound graphs.