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Diskretnyi Analiz i Issledovanie Operatsii, 2014, Volume 21, Issue 3, Pages 41–52 (Mi da774)  
This article is cited in 35 scientific papers (total in 35 papers)

FPTAS for solving a problem of search for a vector subset

A. V. Kel'manovab, S. M. Romanchenkoab

a S. L. Sobolev Institute of Mathematics, SB RAS, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
b Novosibirsk State University, 2 Pirogov St., 630090 Novosibirsk, Russia
Full-text PDF (253 kB) Citations (35)
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Abstract: We consider one NP-hard problem of searching for a vector subset in a given finite Euclidean vector set. It is assumed that the desired subset has a fixed cardinality and contains vectors close to the subset center under the criterion of the minimum sum-of-squared distances. The subset center is defined as the mean value of elements of required subsets. We prove that (unless P$=$NP) there are no fully polynomial time approximation scheme (FPTAS) for the general case of the problem. FPTAS for the case of fixed space dimension is presented. Bibliogr. 12.
Keywords: search for a vector subset, Euclidean space, minimum sum-of-squared distances, NP-hardness, FPTAS.
Received: 11.11.2013
Revised: 29.01.2014
English version:
Journal of Applied and Industrial Mathematics, 2014, Volume 8, Issue 3, Pages 329–336
DOI: https://doi.org/10.1134/S1990478914030041
Bibliographic databases:
Document Type: Article
UDC: 519.16+519.85
Language: Russian
Citation: A. V. Kel'manov, S. M. Romanchenko, “FPTAS for solving a problem of search for a vector subset”, Diskretn. Anal. Issled. Oper., 21:3 (2014), 41–52; J. Appl. Industr. Math., 8:3 (2014), 329–336
Citation in format AMSBIB
\Bibitem{KelRom14}
\by A.~V.~Kel'manov, S.~M.~Romanchenko
\paper FPTAS for solving a~problem of search for a~vector subset
\jour Diskretn. Anal. Issled. Oper.
\yr 2014
\vol 21
\issue 3
\pages 41--52
\mathnet{http://mi.mathnet.ru/da774}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=3242100}
\transl
\jour J. Appl. Industr. Math.
\yr 2014
\vol 8
\issue 3
\pages 329--336
\crossref{https://doi.org/10.1134/S1990478914030041}
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    • This publication is cited in the following 35 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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