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Diskretn. Anal. Issled. Oper., 2013, Volume 20, Number 4, Pages 36–45 (Mi da738)  

This article is cited in 10 scientific papers (total in 10 papers)

A $2$-approximation polynomial algorithm for one clustering problem

A. V. Kelmanovab, V. I. Khandeevb

a Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
b Novosibirsk State University, 2 Pirogov St., 630090 Novosibirsk, Russia

Abstract: A $2$-approximation algorithm is presented for one NP-hard data analysis problem. Namely, the problem is to partition a set of Euclidean vectors into two subsets (clusters) under the criterion of minimum sum-of-squares of distances from the elements of clusters to their centers. The center of the first cluster is the average value of vectors in the cluster and the center of the second one is 0. Bibliogr. 16.

Keywords: cluster analysis, search for a vector subset, computational complexity, approximation polynomial algorithm.

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English version:
Journal of Applied and Industrial Mathematics, 2013, 7:4, 515–521

Bibliographic databases:

UDC: 519.2+621.391
Received: 12.06.2012
Revised: 21.10.2012

Citation: A. V. Kelmanov, V. I. Khandeev, “A $2$-approximation polynomial algorithm for one clustering problem”, Diskretn. Anal. Issled. Oper., 20:4 (2013), 36–45; J. Appl. Industr. Math., 7:4 (2013), 515–521

Citation in format AMSBIB
\Bibitem{KelKha13}
\by A.~V.~Kelmanov, V.~I.~Khandeev
\paper A $2$-approximation polynomial algorithm for one clustering problem
\jour Diskretn. Anal. Issled. Oper.
\yr 2013
\vol 20
\issue 4
\pages 36--45
\mathnet{http://mi.mathnet.ru/da738}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3114911}
\transl
\jour J. Appl. Industr. Math.
\yr 2013
\vol 7
\issue 4
\pages 515--521
\crossref{https://doi.org/10.1134/S1990478913040066}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Orlov, “Chislennyi poisk globalnykh reshenii v zadachakh nesimmetrichnoi bilineinoi otdelimosti”, Diskretn. analiz i issled. oper., 22:1 (2015), 64–85  mathnet  crossref  mathscinet  elib
    2. A. V. Kel'manov, S. A. Khamidullin, “An approximation polynomial-time algorithm for a sequence bi-clustering problem”, Comput. Math. Math. Phys., 55:6 (2015), 1068–1076  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. A. V. Kel'manov, V. I. Khandeev, “An exact pseudopolynomial algorithm for a bi-partitioning problem”, J. Appl. Industr. Math., 9:4 (2015), 497–502  mathnet  crossref  crossref  mathscinet  elib
    4. A. V. Kel'manov, V. I. Khandeev, “A randomized algorithm for two-cluster partition of a set of vectors”, Comput. Math. Math. Phys., 55:2 (2015), 330–339  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. A. V. Kel'manov, V. I. Khandeev, “Fully polynomial-time approximation scheme for a special case of a quadratic Euclidean 2-clustering problem”, Comput. Math. Math. Phys., 56:2 (2016), 334–341  mathnet  crossref  crossref  isi  elib
    6. A. V. Kel'manov, A. V. Motkova, “Exact pseudopolinomial algorithms for a balanced $2$-clustering problem”, J. Appl. Industr. Math., 10:3 (2016), 349–355  mathnet  crossref  crossref  mathscinet  elib
    7. A. Kel'manov, V. Khandeev, “Some algorithms with guaranteed accuracy for 2-clustering problems with given center of one cluster”, 2017 International Multi-Conference on Engineering, Computer and Information Sciences (SIBIRCON), IEEE, 2017, 91–93  crossref  isi
    8. A. Kel'manov, A. Motkova, “An approximation polynomial-time algorithm for a cardinality-weighted 2-clustering problem”, 2017 International Multi-Conference on Engineering, Computer and Information Sciences (SIBIRCON), IEEE, 2017, 94–96  crossref  isi
    9. A. V. Eremeev, A. V. Kel'manov, A. V. Pyatkin, “On complexity of searching a subset of vectors with shortest average under a cardinality restriction”, Analysis of Images, Social Networks and Texts, AIST 2016, Communications in Computer and Information Science, 661, ed. D. Ignatov, M. Khachay, V. Labunets, N. Loukachevitch, S. Nikolenko, A. Panchenko, A. Savchenko, K. Vorontsov, Springler, 2017, 51–57  crossref  mathscinet  isi  scopus
    10. A. V. Kel'manov, A. V. Motkova, “Polynomial-time approximation algorithm for the problem of cardinality-weighted variance-based 2-clustering with a given center”, Comput. Math. Math. Phys., 58:1 (2018), 130–136  mathnet  crossref  crossref  isi  elib
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