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A note on the parametric maximum flow problem and some related reoptimization issues

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  • Maria Scutellà

Abstract

In this paper, we will extend the results about the parametric maximum flow problem to networks in which the parametrization of the arc capacities can involve both the source and the sink, as in Gallo, Grigoriadis, and Tarjan (1989), and also an additional node. We will show that the minimum cuts of the investigated networks satisfy a relaxed form of the generalized nesting property (Arai, Ueno, and Kajitani, 1993). A consequence is that the corresponding parametric maximum flow value function has at most n −1 breakpoints. All the minimum cut capacities can therefore be computed by O(1) maximum flow computations. We will show then that, given O(n) increasing values of the parameter, it is possible to compute the corresponding maximum flows by O(1) maximum flow computations, by suitably extending Goldberg and Tarjan’s maximum flow algorithm. Copyright Springer Science+Business Media, LLC 2007

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  • Maria Scutellà, 2007. "A note on the parametric maximum flow problem and some related reoptimization issues," Annals of Operations Research, Springer, vol. 150(1), pages 231-244, March.
    • Handle: RePEc:spr:annopr:v:150:y:2007:i:1:p:231-244:10.1007/s10479-006-0155-z
    DOI: 10.1007/s10479-006-0155-z
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    References listed on IDEAS

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    1. S. Thomas McCormick, 1999. "Fast Algorithms for Parametric Scheduling Come From Extensions to Parametric Maximum Flow," Operations Research, INFORMS, vol. 47(5), pages 744-756, October.
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    Cited by:

    1. Nir Halman & Mikhail Y. Kovalyov & Alain Quilliot, 2023. "Max–max, max–min, min–max and min–min knapsack problems with a parametric constraint," 4OR, Springer, vol. 21(2), pages 235-246, June.

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    Keywords

    Maximum flow; Parametric arc capacity;

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