On finding lowest common ancestors: simplification and parallelization
SIAM Journal on Computing
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
A unified approach to approximating resource allocation and scheduling
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Journal of Experimental Algorithmics (JEA)
Approximating the Throughput of Multiple Machines in Real-Time Scheduling
SIAM Journal on Computing
The Maximum Edge-Disjoint Paths Problem in Bidirected Trees
SIAM Journal on Discrete Mathematics
Disjoint paths in densely embedded graphs
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Approximation algorithms for disjoint paths problems
Approximation algorithms for disjoint paths problems
Conversion of coloring algorithms into maximum weight independent set algorithms
Discrete Applied Mathematics
Conversion of coloring algorithms into maximum weight independent set algorithms
Discrete Applied Mathematics
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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 unbounded degree, even if all weights are the same (the unweighted case). Three different approximation algorithms are implemented: a known combinatorial (5/3 + ε)-approximation algorithm A1 for the unweighted case, a new combinatorial 2-approximation algorithm A2 for the weighted case, and a known (5/3 + ε)-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/ε √n ċ m) 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.