Combinatorial OptimizationView this Special Issue
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
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 , a valid perturbation of is a convex function that can be substituted for in the total cost function without violating the optimality of . Tolerance set for an is the collection of all valid perturbations of . We characterize the tolerance set for each in terms of nonsingleton shortest distances between nodes and . We also give an efficient algorithm to compute the nonsingleton shortest distances between all pairs of nodes in time where denotes the number of nodes in the given graph.
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