Optimal Wavelength Routing on Directed Fiber Trees

We present a polynomial time greedy algorithm that assigns proper wavelengths to a set of requests of maximum load L per directed ber link on a directed ber tree using at most 5=3L wavelengths. This improves previous results of 12, 10, 8, 9]. We also prove that no greedy algorithm can in general use less than 5=3L wavelengths for a set of requests of load L in a directed ber tree, and thus our algorithm is optimal in the class of greedy algorithms which includes the algorithms presented in 12, 10, 8, 9].