Article ID: | iaor20162818 |
Volume: | 68 |
Issue: | 2 |
Start Page Number: | 121 |
End Page Number: | 129 |
Publication Date: | Sep 2016 |
Journal: | Networks |
Authors: | Orlin James B, Pfetsch Marc E, Joormann Imke |
Keywords: | networks: flow, combinatorial optimization, programming: linear |
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.