Advances in Decision Sciences

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Combinatorial Optimization

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Volume 2005 |Article ID 861343 | https://doi.org/10.1155/JAMDS.2005.83

P. T. Sokkalingam, Prabha Sharma, "A combinatorial arc tolerance analysis for network flow problems", Advances in Decision Sciences, vol. 2005, Article ID 861343, 12 pages, 2005. https://doi.org/10.1155/JAMDS.2005.83

A combinatorial arc tolerance analysis for network flow problems

Received10 Jul 2002
Revised15 May 2003

Abstract

For the separable convex cost flow problem, we consider the problem of determining tolerance set for each arc cost function. For a given optimal flow x, a valid perturbation of cij(x) is a convex function that can be substituted for cij(x) in the total cost function without violating the optimality of x. Tolerance set for an arc(i,j) is the collection of all valid perturbations of cij(x). We characterize the tolerance set for each arc(i,j) in terms of nonsingleton shortest distances between nodes i and j. We also give an efficient algorithm to compute the nonsingleton shortest distances between all pairs of nodes in O(n3) time where n denotes the number of nodes in the given graph.

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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