### Implementation of approximation algorithms for weighted and unweighted edge-disjoint paths in bidirected treesImplementation of approximation algorithms for weighted and unweighted edge-disjoint paths in bidirected trees

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 Author Erlebach, Thomas ♦ Jansen, Klaus Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2002 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Computer programming, programs & data Subject Keyword Algorithms ♦ Combinatorial optimization ♦ Experimentation ♦ Linear programming Abstract 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 $\textit{NP}-$ 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 $\textit{A}1$ for the unweighted case, a new combinatorial 2-approximation algorithm $\textit{A}2$ for the weighted case, and a known (5/3 + ε)-approximation algorithm $\textit{A}3$ for the weighted case that is based on linear programming. For algorithm $\textit{A}1,$ it is shown how efficient data structures can be used to obtain a worst-case running-time of O(m + n + $4^{1/ε}$ √n ċ m) for instances consisting of $\textit{m}$ paths in a tree with $\textit{n}$ 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. ISSN 10846654 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2002-12-01 Publisher Place New York e-ISSN 10846654 Journal Journal of Experimental Algorithmics (JEA) Volume Number 7 Starting Page 6

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Source: ACM Digital Library