On the 1.1 edge-coloring of multigraphs
SIAM Journal on Discrete Mathematics
Efficient routing in all-optical networks
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
LEDA: a platform for combinatorial and geometric computing
Communications of the ACM
A note on optical routing on trees
Information Processing Letters
Bipartite Edge Coloring in $O(\Delta m)$ Time
SIAM Journal on Computing
Optimal wavelength routing on directed fiber trees
Theoretical Computer Science
Improved access to optical bandwidth in trees
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
The complexity of path coloring and call scheduling
Theoretical Computer Science
Efficient Wavelength Routing on Directed Fiber Trees
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Efficient access to optical bandwidth
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Call Scheduling in Trees, Rings and Meshes
HICSS '97 Proceedings of the 30th Hawaii International Conference on System Sciences: Software Technology and Architecture - Volume 1
Journal of Experimental Algorithmics (JEA)
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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 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 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.