A characterization of irreducible infeasible subsystems in flow networks
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Flow-Networks-iis-James-Orlin.pdf
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Author(s)
Joormann, Imke
Pfetsch, Marc E.
Orlin, James B
Date Issued
August 2016
Journal
Networks
Publisher
Wiley Blackwell
Citation
Joormann, Imke et al. “A Characterization of Irreducible Infeasible Subsystems in Flow Networks.” Networks 68, 2 (June 2016): 121–129 © 2016 Wiley Periodicals, Inc
Version
Author's final manuscript
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 NP-hard.
MIT Department
Sloan School of Management
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1002/net.21686
