Geodesic
On the belonging of the problems MIN-PC and MASC-GP$(n)$ to the class of MAX-SNP-hard problems
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 3, pp. 210-216
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

It is known that the problem on the minimal covering of a finite number of points in a plane by a set of straight lines (MIN-PC) and the problem on the minimal affine separating committee formulated in a space of fixed dimension (MASC-GP$(n)$) are NP-hard in the strong sense. We show that these problems are MAX-SNP-hard.
Keywords: computational complexity, strong NP-hardness, covering of points, affine committee. 
@article{TIMM_2010_16_3_a22,
     author = {M. I. Poberii},
     title = {On the belonging of the problems {MIN-PC} and {MASC-GP}$(n)$ to the class of {MAX-SNP-hard} problems},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {210--216},
     year = {2010},
     volume = {16},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2010_16_3_a22/}
}
TY  - JOUR
AU  - M. I. Poberii
TI  - On the belonging of the problems MIN-PC and MASC-GP$(n)$ to the class of MAX-SNP-hard problems
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2010
SP  - 210
EP  - 216
VL  - 16
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TIMM_2010_16_3_a22/
LA  - ru
ID  - TIMM_2010_16_3_a22
ER  - 
%0 Journal Article
%A M. I. Poberii
%T On the belonging of the problems MIN-PC and MASC-GP$(n)$ to the class of MAX-SNP-hard problems
%J Trudy Instituta matematiki i mehaniki
%D 2010
%P 210-216
%V 16
%N 3
%U http://geodesic.mathdoc.fr/item/TIMM_2010_16_3_a22/
%G ru
%F TIMM_2010_16_3_a22
M. I. Poberii. On the belonging of the problems MIN-PC and MASC-GP$(n)$ to the class of MAX-SNP-hard problems. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 3, pp. 210-216. http://geodesic.mathdoc.fr/item/TIMM_2010_16_3_a22/

[1] Megiddo N., Tamir A., “On the complexity of locating linear facilities in the plane”, Oper. Res. Lett., 1:5 (1982), 194–197 | DOI | MR | Zbl

[2] Khachai M. Yu., “Computational and approximational complexity of combinatorial problems related to the committee polyhedral separability of finite sets”, Pattern Recognition and Image Analysis, 18:2 (2008), 237–242 | DOI | MR

[3] Khachay M., Poberii M., “Complexity and approximability of committee polyhedral separability of sets in general position”, Informatica, 20:2 (2009), 217–234 | MR | Zbl

[4] Papadimitriou C., Yannakakis M., “Optimization, approximation, and complexity classes”, J. Comput. System Sci., 43:3 (1991), 425–440 | DOI | MR | Zbl

[5] Geri M., Dzhonson D., Vychislitelnye mashiny i trudnoreshaemye zadachi, Mir, M., 1982, 439 pp. | MR

[6] Mazurov Vl. D., “Komitety sistem neravenstv i zadacha raspoznavaniya”, Kibernetika, 1971, no. 3, 140–146 | MR | Zbl

[7] Khachai M. Yu., “O vychislitelnoi slozhnosti zadachi o minimalnom komitete i smezhnykh zadach”, Dokl. RAN, 406:6 (2006), 742–745 | MR | Zbl

[8] Vazirani V., Approximation algorithms, Springer, Berlin, 2001, 378 pp. | MR

[9] Kumar Anil V. S., Arya Sunil, Ramesh H., “Hardness of set cover with intersection 1”, Proc. 27-th International Colloquium on Automata, Languages and Programming, LNCS, 1853, 2000, 624–635 | MR | Zbl