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

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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.

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  1. Dipartimento di Informatica, Largo B. Pontecorvo 3, I-56127, Pisa, Italy

    Maria Grazia Scutellà

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  1. Maria Grazia Scutellà
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Correspondence to Maria Grazia Scutellà.

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Scutellà, M.G. A note on the parametric maximum flow problem and some related reoptimization issues. Ann Oper Res 150, 231–244 (2007). https://doi.org/10.1007/s10479-006-0155-z

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  • DOI: https://doi.org/10.1007/s10479-006-0155-z

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