Strong duality for the maximum Borel flow problem

Authors:
Ronald Koch;Ebrahim Nasrabadi
Affiliations:
Technische Universität Berlin, Institut für Mathematik, Berlin, Germany;Technische Universität Berlin, Institut für Mathematik, Berlin, Germany
Venue:
INOC'11 Proceedings of the 5th international conference on Network optimization
Year:
2011

Citing 2
Cited 0

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Abstract

Research on flows over time has been conducted mainly in two separate and independent approaches, namely discrete and continuous models, depending on whether a discrete or continuous representation of time is used. Recently, Borel flows have been introduced to build a bridge between these two models. In this paper, we consider the maximum Borel flow problem formulated in a network where capacities on arcs are given as Borel measures and storage might be allowed at the nodes of the network. This problem is formulated as a linear program in a space of measures. We define a dual problem and prove a strong duality result.We show that strong duality is closely related to a MaxFlow-MinCut Theorem.