On the Complexity of Wavelength Converters

In this paper we present a greedy wavelength routing algorithm that allocates a total bandwidth of w(l) wavelengths to any set of requests of load l (where load is defined as the maximum number of requests that go through any directed fiber link) and we give sufficient conditions for correct operation of the algorithm when applied to binary tree networks. We exploit properties of Ramanujan graphs to show that (for the case of binary tree networks) our algorithm increases the bandwidth utilized compared to the algorithm presented in [3]. Furthermore, we use another class of graphs called dispersers, to implement wavelength converters of asymptotically optimal complexity with respect to their size (the number of all possible conversions). We prove that their use leads to optimal and nearly-optimal bandwidth allocation even in a greedy manner.

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