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The partial inverse minimum cut problem with L 1-norm is strongly NP-hard

Published online by Cambridge University Press:  25 October 2010

Elisabeth Gassner
Elisabeth Gassner*
Affiliation:
Department of Optimization and Discrete Mathematics, Graz University of Technology, Steyrergasse 30, 8010 Graz, Austria. gassner@opt.math.tu-graz.ac.at
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Abstract

The partial inverse minimum cut problem is to minimally modify the capacities of a digraph such that there exists a minimum cut with respect to the new capacities that contains all arcs of a prespecified set. Orlin showed that the problem is strongly NP-hard if the amount of modification is measured by the weighted L 1-norm. We prove that the problem remains hard for the unweighted case and show that theNP-hardness proof of Yang [RAIRO-Oper. Res.35 (2001) 117–126] for this problem with additionalbound constraints is notcorrect.

Keywords

Partial inverse minimum cut problem
Type
Research Article
Information
RAIRO - Operations Research , Volume 44 , Issue 3 , July 2010 , pp. 241 - 249
Copyright
© EDP Sciences, ROADEF, SMAI, 2010

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References

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