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.

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
Mots-clés : partial inverse minimum cut problem 
@article{RO_2010__44_3_241_0,
     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://www.numdam.org/articles/10.1051/ro/2010017/}
}
TY  - JOUR
AU  - Gassner, Elisabeth
TI  - The partial inverse minimum cut problem with L1-norm is strongly NP-hard
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2010
SP  - 241
EP  - 249
VL  - 44
IS  - 3
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ro/2010017/
DO  - 10.1051/ro/2010017
LA  - en
ID  - RO_2010__44_3_241_0
ER  - 
%0 Journal Article
%A Gassner, Elisabeth
%T The partial inverse minimum cut problem with L1-norm is strongly NP-hard
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2010
%P 241-249
%V 44
%N 3
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ro/2010017/
%R 10.1051/ro/2010017
%G en
%F RO_2010__44_3_241_0
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. http://www.numdam.org/articles/10.1051/ro/2010017/

[1] R.K. Ahuja and J.B. Orlin, Inverse optimization. Oper. Res. 49 (2001) 771-783. | Zbl

[2] L.R. Ford, Jr. and D.R. Fulkerson, Maximal flow through a network. Canad. J. Math. 8 (1956) 399-404. | Zbl

[3] M.R. Garey, D.S. Johnson and L. Stockmeyer, Some simplified NP-complete graph problems. Theor. Comput. Sci. 1 (1976) 237-267. | Zbl

[4] C. Heuberger, Inverse combinatorial optimization: a survey on problems, methods, and results. J. Comb. Optim. 8 (2004) 329-361. | Zbl

[5] T.C. Lai and J.B. Orlin, The complexity of preprocessing. Research Report of Sloan School of Management, MIT (2003).

[6] J.B. Orlin, Partial inverse optimization problems. Working paper, Sloan School of Management, MIT.

[7] X. Yang, Complexity of partial inverse assignment problem and partial inverse cut problem. RAIRO-Oper. Res. 35 (2001) 117-126. | Numdam | Zbl

[8] J. Zhang and M.-C. Cai, Inverse problem of minimum cuts. Math. Methods Oper. Res. 47 (1998) 51-58. | Zbl

Cité par Sources :