Bandwidth Allocation Algorithms on Tree-Shaped All-Optical Networks with Wavelength Converters

In this paper we consider the problem of allocating optical bandwidth on a tree-shaped network when wavelength conversion is allowed. We consider both converters with full conversion capabilities and converters with limited capabilities. We give upper and lower bounds on the number of full wavelength converters necessary to fully utilize the optical bandwidth available. For converters of limited capabilities we show that, for general trees, converters of degree dL=3e + 1 are suucient to route a set of requests of load L using at most 3=2L wavelengths. For the special case of binary trees, we show that converters of degree O(p L) are suucient to route a set of requests of load L using exactly L wavelengths. The study of limited capabilities converters is based on graph construction problems that might be of their own interest.