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Diskretnyi Analiz i Issledovanie Operatsii, 2016, Volume 23, Issue 3, Pages 21–34
DOI: https://doi.org/10.17377/daio.2016.23.520 (Mi da850) 		 
This article is cited in 14 scientific papers (total in 14 papers)

Exact pseudopolinomial algorithms for a balanced $2$-clustering problem

A. V. Kel'manovab, A. V. Motkovab

a Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
b Novosibirsk State University, 2 Pirogov St., 630090 Novosibirsk, Russia
Full-text PDF (260 kB) Citations (14)
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DOI: https://doi.org/10.17377/daio.2016.23.520
Abstract: We consider the strongly NP-hard problem of partitioning a set of Euclidean points into two clusters so as to minimize the sum (over both clusters) of the weighted sum of the squared intracluster distances from the elements of the clusters to their centers. The weights of sums are the sizes of the clusters. The center of one cluster is given as input, while the center of the other cluster is unknown and determined as the average value over all points in the cluster (the geometric center). The two versions of the problems are analyzed in which the cluster sizes are either parts of the input or optimization variables. We present and prove exact pseudopolynomial algorithms in the case of integer components of the input points and fixed space dimension. Bibliogr. 24.
Keywords: Euclidean space, balanced clustering, NP-hardness, integer inputs, fixed space dimension, exact pseudopolynomial algorithm.
Funding agency Grant number
Russian Science Foundation 16-11-10041
Received: 25.05.2016
English version:
Journal of Applied and Industrial Mathematics, 2016, Volume 10, Issue 3, Pages 349–355
DOI: https://doi.org/10.1134/S1990478916030054
Bibliographic databases:
Document Type: Article
UDC: 519.16+519.85
Language: Russian
Citation: A. V. Kel'manov, A. V. Motkova, “Exact pseudopolinomial algorithms for a balanced $2$-clustering problem”, Diskretn. Anal. Issled. Oper., 23:3 (2016), 21–34; J. Appl. Industr. Math., 10:3 (2016), 349–355
Citation in format AMSBIB
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\by A.~V.~Kel'manov, A.~V.~Motkova
\paper Exact pseudopolinomial algorithms for a~balanced $2$-clustering problem
\jour Diskretn. Anal. Issled. Oper.
\yr 2016
\vol 23
\issue 3
\pages 21--34
\mathnet{http://mi.mathnet.ru/da850}
\crossref{https://doi.org/10.17377/daio.2016.23.520}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3563714}
\elib{https://elibrary.ru/item.asp?id=26129765}
\transl
\jour J. Appl. Industr. Math.
\yr 2016
\vol 10
\issue 3
\pages 349--355
\crossref{https://doi.org/10.1134/S1990478916030054}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84983502949}
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Дискретный анализ и исследование операций
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