Revisiting parametric multi-terminal problems: Maximum flows, minimum cuts and cut-tree computations

Authors:
D. Barth;P. Berthomé;M. Diallo;A. Ferreira
Affiliations:
Laboratoire PRiSM, UMR 8144, CNRS, Université de Versailles, 45 Av. des Etats-Unis, 78035 Versailles-Cedex, France;Laboratoire de Recherche en Informatique (LRI), UMR 8623, CNRS, Université Paris-Sud, 91405, Orsay-Cedex, France;Depto. Eng. Industrial, Pontifícia Universidade Católica (PUC-RIO) Rua Marquês de São Vicente, 225, Gávea Rio de Janeiro, RJ - 22453-900, Brazil;COST Office, Avenue Louise 149, 1050 Brussels, Belgium
Venue:
Discrete Optimization
Year:
2006

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Abstract

Given an undirected network, the multi-terminal network flows analysis consists in determining the all pairs maximum flow values. In this paper, we consider an undirected network in which some edge capacities are allowed to vary and we analyze the impact of such variations on the all pairs maximum flow values. We first provide an efficient algorithm for the single parametric capacity case, and then propose a generalization to the case of multiple parametric capacities. Moreover, we provide a study on Gomory-Hu cut-tree relationships.