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Diskretnyi Analiz i Issledovanie Operatsii, Ser. 2, 2007, Volume 14, Issue 1, Pages 32–42 (Mi da54)  
This article is cited in 28 scientific papers (total in 28 papers)

The problem of finding a subset of vectors with the maximum total weight

A. E. Baburin, E. Kh. Gimadi, N. I. Glebov, A. V. Pyatkin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (241 kB) Citations (28)
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Abstract: The NP-hardness is proved for the discrete optimization problems connected with maximizing the total weight of a subset of a finite set of vectors in Euclidean space, i.e., the Euclidean norm of the sum of the members. Two approximation algorithms are suggested, and the bounds for the relative error and time complexity are obtained. We give a polynomial approximation scheme in the case of a fixed dimension and distinguished a subclass of problems solvable in pseudopolynomial time. The results obtained are useful for solving the problem of choice of a fixed number of subsequences from a numerical sequence with a given number of quasiperiodical repetitions of the subsequence.
Received: 07.12.2006
Revised: 16.05.2007
English version:
Journal of Applied and Industrial Mathematics, 2008, Volume 2, Issue 1, Pages 32–38
DOI: https://doi.org/10.1007/s11754-008-1004-3
Bibliographic databases:
UDC: 519.854
Language: Russian
Citation: A. E. Baburin, E. Kh. Gimadi, N. I. Glebov, A. V. Pyatkin, “The problem of finding a subset of vectors with the maximum total weight”, Diskretn. Anal. Issled. Oper., Ser. 2, 14:1 (2007), 32–42; J. Appl. Industr. Math., 2:1 (2008), 32–38
Citation in format AMSBIB
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\paper The problem of finding a subset of vectors with the maximum total weight
\jour Diskretn. Anal. Issled. Oper., Ser.~2
\yr 2007
\vol 14
\issue 1
\pages 32--42
\mathnet{http://mi.mathnet.ru/da54}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2392668}
\zmath{https://zbmath.org/?q=an:1249.90211}
\transl
\jour J. Appl. Industr. Math.
\yr 2008
\vol 2
\issue 1
\pages 32--38
\crossref{https://doi.org/10.1007/s11754-008-1004-3}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-41749104288}
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    • This publication is cited in the following 28 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Дискретный анализ и исследование операций
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