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 Diskretn. Anal. Issled. Oper., 2014, Volume 21, Number 1, Pages 53–66 (Mi da760)

Approximation algorithm for one problem of partitioning a sequence

A. V. Kelmanovab, S. A. Khamidullinb

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

Abstract: We consider one NP-hard problem of partitioning of a finite Euclidean vectors sequence into two clusters minimizing the sum of squared distances from the clusters elements to their centers. The cardinalities of the clusters are fixed. The center of the first cluster is defined as the mean value of all vectors in a cluster. The center of the second cluster is given in advance and is equal to 0. Additionally, the partition must satisfy the restriction that for all vectors that are in the first cluster the difference between the indices of two consequent vectors from this cluster is bounded from below and above by some constants. An effective $2$-approximation algorithm for the problem is presented. Bibliogr. 9.

Keywords: Euclidean vectors sequence, ñlusterization, minimum sum-of-squared distances, NP-hardness, effective $2$-approximation algorithm.

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English version:
Journal of Applied and Industrial Mathematics, 2014, 8:2, 236–244

Bibliographic databases:

UDC: 519.16+519.85
Revised: 13.05.2013

Citation: A. V. Kelmanov, S. A. Khamidullin, “Approximation algorithm for one problem of partitioning a sequence”, Diskretn. Anal. Issled. Oper., 21:1 (2014), 53–66; J. Appl. Industr. Math., 8:2 (2014), 236–244

Citation in format AMSBIB
\Bibitem{KelKha14} \by A.~V.~Kelmanov, S.~A.~Khamidullin \paper Approximation algorithm for one problem of partitioning a~sequence \jour Diskretn. Anal. Issled. Oper. \yr 2014 \vol 21 \issue 1 \pages 53--66 \mathnet{http://mi.mathnet.ru/da760} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3288381} \transl \jour J. Appl. Industr. Math. \yr 2014 \vol 8 \issue 2 \pages 236--244 \crossref{https://doi.org/10.1134/S1990478914020100} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84902178105} 

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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. Kel'manov, S. A. Khamidullin, V. I. Khandeev, “Fully polynomial-time approximation scheme for a sequence $2$-clustering problem”, J. Appl. Industr. Math., 10:2 (2016), 209–219
2. A. V. Kel'manov, L. V. Mikhailova, S. A. Khamidullin, V. I. Khandeev, “An approximation algorithm for the problem of partitioning a sequence into clusters with constraints on their cardinalities”, Proc. Steklov Inst. Math. (Suppl.), 299, suppl. 1 (2017), 88–96
3. A. V. Kel'manov, S. A. Khamidullin, V. I. Khandeev, “Exact pseudopolynomial algorithm for one sequence partitioning problem”, Autom. Remote Control, 78:1 (2017), 67–74
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
5. A. V. Kel'manov, S. A. Khamidullin, V. I. Khandeev, “A randomized algorithm for a sequence 2-clustering problem”, Comput. Math. Math. Phys., 58:12 (2018), 2078–2085
6. A. Kel'manov, S. Khamidullin, V. Khandeev, “A randomized algorithm for 2-partition of a sequence”, Analysis of Images, Social Networks and Texts, AIST 2017, Lecture Notes in Computer Science, 10716, eds. W. van der Aalst, D. Ignatov, M. Khachay, S. Kuznetsov, V. Lempitsky, I. Lomazova, N. Loukachevitch, A. Napoli, A. Panchenko, P. Pardalos, A. Savchenko, S. Wasserman, Springer, 2018, 313–322
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