A characterization of irreducible infeasible subsystems in flow networks

A characterization of irreducible infeasible subsystems in flow networks

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Article ID: iaor20162818
Volume: 68
Issue: 2
Start Page Number: 121
End Page Number: 129
Publication Date: Sep 2016
Journal: Networks
Authors: , ,
Keywords: networks: flow, combinatorial optimization, programming: linear
Abstract:

Infeasible network flow problems with supplies and demands can be characterized via violated cut‐inequalities of the classical Gale‐Hoffman theorem. Written as a linear program, irreducible infeasible subsystems (IISs) provide a different means of infeasibility characterization. In this article, we answer a question left open in the literature by showing a one‐to‐one correspondence between IISs and Gale‐Hoffman‐inequalities in which one side of the cut has to be weakly connected. We also show that a single max‐flow computation allows one to compute an IIS. Moreover, we prove that finding an IIS of minimal cardinality in this special case of flow networks is strongly N P ‐hard.

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