Efficient routing in all-optical networks
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Improved bounds for the unsplittable flow problem
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Improved approximations for edge-disjoint paths, unsplittable flow, and related routing problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Journal of Computer and System Sciences
Hardness of the undirected edge-disjoint paths problem
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Forwarding and optical indices of a graph
Discrete Applied Mathematics
Journal of Computer and System Sciences
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In this paper, we consider the undirected version of the well known maximum edge-disjoint paths problem, restricted to complete graphs. We propose an off-line 3.75-approximation algorithm and an on-line 6.47-approximation algorithm, improving the earlier 9-approximation algorithm proposed by Carmi, Erlebach, and Okamoto [P. Carmi, T. Erlebach, Y. Okamoto, Greedy edge-disjoint paths in complete graphs, in: Proc. 29th Workshop on Graph Theoretic Concepts in Computer Science, in: LNCS, vol. 2880, 2003, pp. 143-155]. Moreover, we show that for the general case, no on-line algorithm is better than a (2-@e)-approximation, for all @e0. For the special case when the number of paths is within a linear factor of the number of vertices of the graph, it is established that the problem can be optimally solved in polynomial time by an off-line algorithm, but that no on-line algorithm is better than a (1.5-@e)-approximation. Finally, the proposed techniques are used to obtain off-line and on-line algorithms with a constant approximation ratio for the related problems of edge congestion routing and wavelength routing in complete graphs.