Complexity and approximability of hyperplane covering problems / Khachay M. // Proceedings of the 4th International Workshop on Image Mining. Theory and Applications, IMTA 2013, In Conjunction with VISIGRAPP 2013. - 2013. - V. , l. . - P. 109-113.

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Conference Paper
Abstract:
The well known N.Megiddo complexity result for Point Cover Problem on the plane is extended onto d-dimensional space (for any fixed d > 1). It is proved that Min-dPC problem is L-reducible to Min-(d + 1)PC problem, therefore for any fixed d < 1 there is no PTAS for Min-dPC problem, unless P = NP.
Author keywords:
Index keywords:
Approximability; Complexity results; Cover problem; Covering problems; D-dimensional spaces
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Affiliations Krasovsky Institute of Mathematics and Mechanics, UB RAS, 16 S. Kovalevskoy St., Ekaterinburg, Russian Federation; Ural Federal University, 19 Mira St., Ekaterinburg, Russian Federation; Omsk State Technical University, 11 Mira Ave., Omsk, Russian Federation
References Agarwal, P.K., Procopiuc, C.M., (2002) Exact and Approximation Algorithms for Clustering, Al-gorithmica, (33), pp. 201-206; Langerman, S., Morin, P., Covering things with things (2005) Discrete Computat. Geom., pp. 717-729; Khachai, M., Computational complexity of recognition learning procedures in the class of piecewise-linear committee decision rules (2010) Automation and Remote Control, 71 (3), pp. 528-539; Vazirany, V., (2001) Approximation Algorithms, , Springer; Johnson, D., Approximation algorithms for combinatorial problems (1974) Journal of Computer and System Sciences, 9 (3), pp. 256-278; LovÁsz, L., On the ratio of integer and fractional covers (1975) Discrete Mathematics, (13), pp. 383-390; Feige, U., A threshold of ln n for approximating set cover (1998) Journal of the ACM, 45 (4), pp. 634-652; Megiddo, N., Tamir, A., On the complexity of locating linear facilities in the plane (1982) Operations Research Letters, 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, , Addison-Wesley; Khachai, M., Poberii, M., Computational complexity of combinatorial problems related to piecewise linear committee pattern recognition learning procedures (2012) Pattern Recognition and Image Analysis, 22 (2), pp. 278-290
Correspondence Address Khachay, M.; Krasovsky Institute of Mathematics and Mechanics, UB RAS, 16 S. Kovalevskoy St., Ekaterinburg, Russian Federation; email: mkhachay@imm.uran.ru
Conference name 4th International Workshop on Image Mining. Theory and Applications, IMTA 2013, In Conjunction with VISIGRAPP 2013
Conference date 23 February 2013 through 23 February 2013
Conference location Barcelona
Conference code 97052
ISBN 9789898565501
Language of Original Document English
Abbreviated Source Title Proc. Int. Workshop Image Min.. Theory Appl., IMTA, Conjunction VISIGRAPP
Source Scopus