| Issue |
RAIRO-Oper. Res.
Volume 44, Number 3, July-September 2010
|
|
|---|---|---|
| Page(s) | 241 - 249 | |
| DOI | https://doi.org/10.1051/ro/2010017 | |
| Published online | 25 October 2010 | |
The partial inverse minimum cut problem with L1-norm is strongly NP-hard
Department of Optimization and Discrete
Mathematics, Graz University of Technology, Steyrergasse 30, 8010 Graz, Austria. gassner@opt.math.tu-graz.ac.at
Received:
22
September
2009
Accepted:
7
August
2010
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 L1-norm. We prove that the problem remains hard for the unweighted case and show that the NP-hardness proof of Yang [RAIRO-Oper. Res. 35 (2001) 117–126] for this problem with additional bound constraints is not correct.
Mathematics Subject Classification: 90C27 / 90C60 / 68Q25
Key words: Partial inverse minimum cut problem
© EDP Sciences, ROADEF, SMAI, 2010
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