On routing of wavebands for all-to-all communications in all-optical paths and cycles

We discuss a model of the all-optical communication technology and an implementation of a simple task, all-to-all, in simple topologies like paths and cycles. The model assumes a single interval (variant of band-pass) filter extracting signal wavelengths for processing and forwarding in intermediate communication nodes. In an attempt to use a minimum number of wavelengths, we give lower and upper bounds on the cardinality of the spectrum used in four cases arising from different assumptions on the topology and the filters. In particular, we propose efficient schedules of directed paths between all pairs of nodes in graphs of maximum node degree two, under the assumption of either a “linear” or “wrapped-around” wavelength spectrum.