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Diskretn. Anal. Issled. Oper., 2012, Volume 19, Number 3, Pages 27–38 (Mi da688)  

This article is cited in 4 scientific papers (total in 4 papers)

Approximation algorithms for some NP-hard problems of searching a vectors subsequence

A. V. Kel'manovab, S. M. Romanchenkoa, S. A. Khamidullina

a S. L. Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: Some NP-hard problems of searching a subsequence in a finite sequence of Euclidean vectors are studied. It is assumed that the desired subsequence has a fixed number of vectors which are mutually close under the criterion of minimum sum of squared distances. Moreover, there is an additional requirement that the difference between the numbers of any two consecutive vectors must lie between two given constants. Some effective 2-approximation algorithms for these problems are presented. Bibliogr. 11.

Keywords: searching a vectors subsequence, minimum sum-of-squared distances, clustering, NP-hardness, effective approximation algorithm.

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English version:
Journal of Applied and Industrial Mathematics, 2012, 6:4, 443–450

Bibliographic databases:

UDC: 519.2+621.391
Received: 11.08.2011
Revised: 07.11.2011

Citation: A. V. Kel'manov, S. M. Romanchenko, S. A. Khamidullin, “Approximation algorithms for some NP-hard problems of searching a vectors subsequence”, Diskretn. Anal. Issled. Oper., 19:3 (2012), 27–38; J. Appl. Industr. Math., 6:4 (2012), 443–450

Citation in format AMSBIB
\Bibitem{KelRomKha12}
\by A.~V.~Kel'manov, S.~M.~Romanchenko, S.~A.~Khamidullin
\paper Approximation algorithms for some NP-hard problems of searching a~vectors subsequence
\jour Diskretn. Anal. Issled. Oper.
\yr 2012
\vol 19
\issue 3
\pages 27--38
\mathnet{http://mi.mathnet.ru/da688}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2986639}
\transl
\jour J. Appl. Industr. Math.
\yr 2012
\vol 6
\issue 4
\pages 443--450
\crossref{https://doi.org/10.1134/S1990478912040059}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Kelmanov, S. M. Romanchenko, S. A. Khamidullin, “Tochnye psevdopolinomialnye algoritmy dlya nekotorykh trudnoreshaemykh zadach poiska podposledovatelnosti vektorov”, Zh. vychisl. matem. i matem. fiz., 53:1 (2013), 143–153  mathnet  crossref  elib
    2. Yu. Yu. Velikanova, “Algoritmy dlya odnoi zadachi o nakhozhdenii maksimuma unimodalnoi funktsii v rezhime online”, Diskretn. analiz i issled. oper., 20:6 (2013), 16–29  mathnet  mathscinet
    3. A. V. Kelmanov, S. M. Romanchenko, S. A. Khamidullin, “An approximation scheme for a problem of finding a subsequence”, Num. Anal. Appl., 10:4 (2017), 313–323  mathnet  crossref  crossref  isi  elib
    4. A. Kel'manov, “Efficient approximation algorithms for some NP-hard problems of partitioning a set and a sequence”, 2017 International Multi-Conference on Engineering, Computer and Information Sciences (SIBIRCON), IEEE, 2017, 87–90  crossref  isi
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