Abstract
Given an undirected edge-weighted n-nodes network in which a single edge-capacity is allowed to vary, Elmaghraby studied the sensitivity analysis of the multi-terminal network flows. The procedure he proposed requires the computation of as many Gomory-Hu cut trees as the number of critical capacities of the edge, leading to a pseudo-polynomial algorithm.
In this paper, we propose a fully polynomial algorithm using only two Gomory-Hu cut trees to solve the Elmaghraby problem and propose an efficient generalization to the case where k edge capacities can vary. We show that obtaining the all-pairs maximum flows, for the case where k edge capacities vary in the network, is polynomial whenever k = O(polylog n), since we show that it can be solved with the computation of 2k Gomory-Hu trees.
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Berthomé, P., Diallo, M., Ferreira, A. (2003). Generalized Parametric Multi-terminal Flows Problem. In: Bodlaender, H.L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2003. Lecture Notes in Computer Science, vol 2880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39890-5_7
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DOI: https://doi.org/10.1007/978-3-540-39890-5_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20452-7
Online ISBN: 978-3-540-39890-5
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