Abstract
Given a number α with 0 < α < 1, a network G = (V, E) and two nodes s and t in G, we consider the problem of finding two disjoint paths P 1 and P 2 from s to t such that length(P1) ≤ length(P 2) and length(P 1) + α·length(P 2) is minimized. The paths may be node-disjoint or edge-disjoint, and the network may be directed or undirected. This problem has applications in reliable communication. We prove an approximation ratio \({1+\alpha} \over {2\alpha}\) for all four versions of this problem, and also show that this ratio cannot be improved for the two directed versions unless P = NP. We also present Integer Linear Programming formulations for all four versions of this problem. For a special case of this problem, we give a polynomial-time algorithm for finding optimal solutions.
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Yang, B., Zheng, S.Q., Lu, E. (2005). Finding Two Disjoint Paths in a Network with Normalized α + -MIN-SUM Objective Function. In: Deng, X., Du, DZ. (eds) Algorithms and Computation. ISAAC 2005. Lecture Notes in Computer Science, vol 3827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11602613_95
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DOI: https://doi.org/10.1007/11602613_95
Publisher Name: Springer, Berlin, Heidelberg
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