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A characterization of irreducible infeasible subsystems in flow networks
Author(s) -
Joormann Imke,
Orlin James B.,
Pfetsch Marc E.
Publication year - 2016
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.21686
Subject(s) - characterization (materials science) , cardinality (data modeling) , flow (mathematics) , computation , mathematics , flow network , computer science , discrete mathematics , mathematical optimization , algebra over a field , algorithm , pure mathematics , data mining , nanotechnology , materials science , geometry
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. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 68(2), 121–129 2016