On finding lowest common ancestors: simplification and parallelization
SIAM Journal on Computing
Approximating the throughput of multiple machines under real-time scheduling
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Optimal wavelength routing on directed fiber trees
Theoretical Computer Science
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Improvements in throughout maximization for real-time scheduling
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
A unified approach to approximating resource allocation and scheduling
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
ICALP '93 Proceedings of the 20th International Colloquium on Automata, Languages and Programming
Maximizing the Number of Connections in Optical Tree Networks
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
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Given a set of weighted directed paths in a bidirected tree, the maximum weight edge-disjoint paths problem (MWEDP) is to select a subset of the given paths such that the selected paths are edge-disjoint and the total weight of the selected paths is maximized. MWEDP is NP-hard for bidirected trees of arbitrary degree, even if all weights are the same (the unweighted case). Three different approximation algorithms are implemented: a known combinatorial (5/3 + Ɛ)-approximation algorithm A1 for the unweighted case, a new combinatorial 2-approximation algorithm A2 for the weighted case, and a known (5/3 + Ɛ)-approximation algorithm A3 for the weighted case that is based on linear programming. For algorithm A1, it is shown how efficient data structures can be used to obtain a worst-case running-time of O(m+n+41/Ɛ√nċm) for instances consisting of m paths in a tree with n nodes. Experimental results regarding the running-times and the quality of the solutions obtained by the three approximation algorithms are reported. Where possible, the approximate solutions are compared to the optimal solutions, which were computed by running CPLEX on an integer linear programming formulation of MWEDP.