Complexity and approximability of committee polyhedral separability of sets in general position / Khachay M., Poberii M. // Informatica. - 2009. - V. 20, l. 2. - P. 217-234.

ISSN:
08684952
Type:
Article
Abstract:
It is known that the minimum affine separating committee (MASC) combinatorial optimization problem, which is related to some machine learning techniques, is NP-hard and does not belong to Apx class unless P=NP. In this paper, it is shown that the MASC problem formulated in a fixed dimension space within n>1 is intractable even if sets defining an instance of the problem are in general position. A new polynomial-time approximation algorithm for this modification of the MASC problem is presented. An approximation ratio and complexity bounds of the algorithm are obtained. © 2009 Institute of Mathematics and Informatics, Vilnius.
Author keywords:
Approximation algorithms; Committees; Computational complexity; Polyhedral separability
Index keywords:
нет данных
DOI:
нет данных
Смотреть в Scopus:
https://www.scopus.com/inward/record.uri?eid=2-s2.0-67651238860&partnerID=40&md5=20d666a80c98678e8c70cae7b2d352a4
Соавторы в МНС:
Другие поля
Поле Значение
Link https://www.scopus.com/inward/record.uri?eid=2-s2.0-67651238860&partnerID=40&md5=20d666a80c98678e8c70cae7b2d352a4
Affiliations Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, S.Kovalevskoy 16, 620219 Ekaterinburg, Russian Federation
Author Keywords Approximation algorithms; Committees; Computational complexity; Polyhedral separability
References Blum, A.L., Rivest, R.L., Training a 3-node neural network is NP-complete (1992) Neural Networks, 5, pp. 117-127; Eremin, I.I., Astafiev, N.N., Introduction into the Theory of Linear and Convex Programming. Phys (1975) Mat. Lit, , in Russian, Moscow, 192 pp; Johnson, D.S., Approximation algorithms for combinatorial problems (1974) Journal of Computer and System Sciences, 9 (3), pp. 256-278; Khachai, M.Y., On the computational complexity of minimum committee problem and related problems (2006) Doklady Mathematics, 73 (1), pp. 138-141; Khachay, M.Y., On the computational and approximational complexity of the minimum affine separating committee problem (2006) Tavricheskii Vestnik Informatiki i Matematiki, 1, pp. 34-43. , in Russian; Khachai, M.Y., Computational and approximational complexity of combinatorial problems related to the committee polyhedral separability of finite sets (2008) Pattern Recognition and Image Analysis, 18 (2), pp. 237-242; Khachai, M.Yu., and M.I. Pobery (2008). Computational complexity and approximability of combinatorial optimization problems connected with committee poplyhedral separability of finite sets. In 20th Intern. Conf. EURO Mini Conf. Continuous Optimiz. & Knowledge-Based Technolog. (EurOPT-2008). Selected papers. Technika, Vilnius. pp. 42-47; Lin, J.H., Vitter, J.S., Complexity results on learning by neural nets (1991) Machine Learning, 6, pp. 211-230; Mazurov, V.D., Committees of inequalities systems and the pattern recognition problem (1971) Kibernetika, 3, pp. 140-146. , in Russian; Megiddo, N., Tamir, A., On the complexity of locating linear facilities in the plane (1982) Operations Research Letters, 5 (1), pp. 194-197; Megiddo, N., On the complexity of polyhedral separability (1988) Discrete and Computational Geometry, 3, pp. 325-337
Correspondence Address Khachay, M.; Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, S.Kovalevskoy 16, 620219 Ekaterinburg, Russian Federation; email: mkhachay@imm.uran.ru
Language of Original Document English
Abbreviated Source Title Informatica
Source Scopus