Efficient Wavelength Routing in Trees with Low { Degree

We study the use of limited wavelength conversion in order to increase bandwidth utilization in WDM (wavelength division multiplexing) all-optical networks. A measure of the complexity of a converter is given by its maximum degree (i.e., the maximum number of potential conversions of any given wavelength). We present trade-oos between the complexityof the converters and the number of wavelengths necessary to route a set of requests as function of the load l in directed ber trees, where load is the maximum number of requests traversing a directed tree link. In particular our results show that it is possible to beat the known lower bounds using constant or poly-logarithmic degree converters and even obtain optimal wavelength routing (i.e., full bandwidth utilization) in case of binary trees using converters of constant degree.