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The ACM Journal of Experimental Algorithmics


Volume 4, Article 4, 1999


Efficient Implementation of an Optimal Greedy Algorithm for Wavelength Assignment in Directed Tree Networks

by

Thomas Erlebach

and

Klaus Jansen

http://www.jea.acm.org/1999/ErlebachWavelength/


Abstract:

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 NP-hard, and the best known polynomial-time approximation algorithm for directed tree networks achieves an approximation ratio of 5/3, which is optimal in the class of greedy algorithms for this problem. We show how the algorithm can be modified in order to improve its running-time to O(Tec(N,L)) for sets of paths with maximum load L in trees with N nodes, where Tec(n,k) is the time for edge-coloring a k-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.

Received
Accepted
Final Revision
Published
April 1, 1999
January 20, 2000
March 8, 2000
May 10, 2000

Last updated and validated May 10, 2000, by editor@jea.acm.org