Department of Optimization and Discrete Mathematics, Graz University of Technology, Steyrergasse 30, 8010 Graz, Austria. firstname.lastname@example.org
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 the NP-hardness proof of Yang [RAIRO-Oper. Res. 35 (2001) 117–126] for this problem with additional bound constraints is not correct.
(Received September 22 2009)
(Accepted August 7 2010)
(Online publication October 25 2010)
Mathematics Subject Classification: