A characterization of irreducible infeasible subsystems in flow networks

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...

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Bibliographic Details
Published inNetworks Vol. 68; no. 2; pp. 121 - 129
Main Authors Joormann, Imke, Orlin, James B., Pfetsch, Marc E.
Format Journal Article
LanguageEnglish
Published New York Blackwell Publishing Ltd 01.09.2016
Wiley Subscription Services, Inc
Subjects
Computation
flow network
Gale-Hoffman theorem
infeasibility analysis
irreducible infeasible subsystem
max flow-min cut
N P ‐hardness
Networks
NP-hardness
Supply and demand
Theorems
witness
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Summary: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
Bibliography:istex:E8DD12E7CC16C67F367E12C1912AF72ABC3D8816
ark:/67375/WNG-0LDXRW8B-1
ArticleID:NET21686
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0028-3045
1097-0037
DOI:10.1002/net.21686