Efficient implementation of an optimal greedy algorithm for wavelength assignment in directed tree networks

In all-optical networks with wavelength-division multiplexing several connections can share a physical link if the signals are transmitted on different wavelengths. As the number of available wavelengths is limited in practice, it is important to find wavelength assignments minimizing the number of different wavelengths used. This path coloring problem is <i>NP</i>-hard, and the best known polynomial-time approximation algorithm for directed tree networks achieves approximation ratio 5/3, which is optimal in the class of greedy algorithms for this problem. It is shown how the algorithm can be modified in order to improve its running-time to <i>O(T<inf>ec</inf>(N,L))</i> for sets of paths with maximum load <i>L</i> in trees with <i>N</i> nodes, where <i>T<inf>ec</inf>(n, k)</i> is the time for edge-coloring a <i>k</i>-regular bipartite graph with n nodes. An implementation of this efficient version of the algorithm in C++ using the LEDA class library is described, and experimental results regarding the running-times and the number of wavelengths used are reported. An additional heuristic that reduces the number of wavelengths used in the average case while maintaining the worst-case bound of 5L/3 is described.

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