Wavelength assignment to minimize requirement on tunable range of optical transceivers in WDM networks

In this paper we consider WDM networks with a tunable transmitter and a fixed-wavelength receiver at each station (similar results hold when the transmitter is fixed and the receiver is tunable). Traditionally, each station is required to be able to access all wavelength channels used in the network. Such requirement limits the number of wavelengths that can be exploited in a WDM network up to the size of the resolvable wavelength set of optical transceivers, which is very limited with current technology. In this paper we observe that this requirement is actually an overkill. To realize a communication topology, physical or logical, it is sufficient that the tunable range of the transmitter at each station covers all the wavelengths of the receivers at its neighboring stations. This observation leads to the study of optimal wavelength assignment to minimize the tunability requirement while still guaranteeing that each receiver has a unique wavelength channel. This optimization problem is shown to NP-complete in general and approximation algorithms with provable performance guarantees are presented. When the communication topologies are complete graphs, de Bruijin digraphs, Kautz digraphs, shuffle or rings, the optimal solutions are provided. Finally, we present tight lower bounds when the communication topology is a hypercube.