The computational complexity and approximability of a series of geometric covering problems / Khachai M.Y., Poberii M.I. // Proceedings of the Steklov Institute of Mathematics. - 2013. - V. 283, l. 1. - P. 64-77.

ISSN:
00815438
Type:
Article
Abstract:
We consider a series of geometric problems of covering finite subsets of finite-dimensional numerical spaces by minimal families of hyperplanes. We prove that the problems are hard and Max-SNP-hard. © 2013 Pleiades Publishing, Ltd.
Author keywords:
L-reduction; Max-SNP-hard problem; NP-complete problem; polynomial-time approximation scheme (PTAS); polynomial-time reduction
Index keywords:
нет данных
DOI:
10.1134/S008154381309006X
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Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russian Federation; Institute of Mathematics and Computer Science, Ural Federal University, pr. Lenina 51, Yekaterinburg, 620000, Russian Federation
Author Keywords L-reduction; Max-SNP-hard problem; NP-complete problem; polynomial-time approximation scheme (PTAS); polynomial-time reduction
References Agarwal, P.K., Procopiuc, C.M., Exact and approximation algorithms for clustering (2002) Algorithmica, 33, pp. 201-206; Langerman, S., Morin, P., Covering things with things (2005) Discrete Comput. Geom., 33 (4), pp. 717-729; Khachai, M.Y., Aspects of the computational complexity of recognition learning procedures in the class of piecewise-linear committee decision rules (2010) Autom. Remote Control, 71 (3), p. 528; Vazirany, V., (2001) Approximation Algorithms, , Berlin: Springer-Verlag; Johnson, D.S., Approximation algorithms for combinatorial problems (1974) J. Comput. System Sci., 9 (3), pp. 256-278; Lovász, L., On the ratio of integer and fractional covers (1975) Discrete Math., 13 (4), pp. 383-390; Feige, U., A threshold of ln n for approximating set cover (1998) J. ACM, 45 (4), pp. 634-652; Megiddo, N., Tamir, A., On the complexity of locating linear facilities in the plane (1982) Oper. Res. Let., 1 (5), pp. 194-197; Papadimitriou, C., Yannakakis, M., Optimization, approximation, and complexity classes (1991) J. Comput. System Sci., 43 (3), pp. 425-440; Papadimitriou, C., (1995) Computational Complexity, , New York: Addison-Wesley; Poberii, M.I., On the belonging of the problems MIN-PC and (MASC-GP(n)) to the class MAX-SNP (2010) Trudy Inst. Mat. Mekh. UrO RAN, 16 (3), p. 210; Schönhage, A., Strassen, V., Schnelle Multiplikation großer Zahlen (1971) Computing, 7 (3-4), pp. 281-292
Correspondence Address Khachai, M. Y.; Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russian Federation; email: mkhachay@imm.uran.ru
Language of Original Document English
Abbreviated Source Title Proc. Steklov Inst. Math.
Source Scopus