Geodesic
The partial inverse minimum cut problem with L1-norm is strongly NP-hard
RAIRO - Operations Research - Recherche Opérationnelle, Tome 44 (2010) no. 3, pp. 241-249

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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.

DOI : 10.1051/ro/2010017
Classification : 90C27, 90C60, 68Q25
Keywords: partial inverse minimum cut problem 
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     author = {Gassner, Elisabeth},
     title = {The partial inverse minimum cut problem with {L1-norm} is strongly {NP-hard}},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {241--249},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {3},
     year = {2010},
     doi = {10.1051/ro/2010017},
     mrnumber = {2762795},
     zbl = {1206.90141},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ro/2010017/}
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Gassner, Elisabeth. The partial inverse minimum cut problem with L1-norm is strongly NP-hard. RAIRO - Operations Research - Recherche Opérationnelle, Tome 44 (2010) no. 3, pp. 241-249. doi: 10.1051/ro/2010017

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