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Diskretn. Anal. Issled. Oper., 2016, Volume 23, Issue 2, Pages 21–40 (Mi da843)  

This article is cited in 5 scientific papers (total in 5 papers)

Fully polynomial-time approximation scheme for a sequence $2$-clustering problem

A. V. Kel'manovab, S. A. Khamidullinb, V. I. Khandeevb

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

Abstract: We consider a strongly NP-hard problem of partitioning a finite sequence of points in Euclidean space into two clusters minimizing the sum over both clusters of intra-cluster sum of squared distances from the clusters elements to their centers. The sizes of the clusters are fixed. The centroid of the first cluster is defined as the mean value of all vectors in the cluster, and the center of the second one is given in advance and is equal to 0. Additionally, the partition must satisfy the restriction that for all vectors in the first cluster the difference between the indices of two consequent points from this cluster is bounded from below and above by some given constants. We present a fully polynomial-time approximation scheme for the case of fixed space dimension. Bibliogr. 27.

Keywords: partitioning, sequence, Euclidean space, minimum sum-of-squared distances, NP-hardness, FPTAS.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-00462

DOI: https://doi.org/10.17377/daio.2016.23.511

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English version:
Journal of Applied and Industrial Mathematics, 2016, 10:2, 209–219

Bibliographic databases:

UDC: 519.16+519.85
Received: 15.09.2015
Revised: 12.01.2016

Citation: A. V. Kel'manov, S. A. Khamidullin, V. I. Khandeev, “Fully polynomial-time approximation scheme for a sequence $2$-clustering problem”, Diskretn. Anal. Issled. Oper., 23:2 (2016), 21–40; J. Appl. Industr. Math., 10:2 (2016), 209–219

Citation in format AMSBIB
\by A.~V.~Kel'manov, S.~A.~Khamidullin, V.~I.~Khandeev
\paper Fully polynomial-time approximation scheme for a~sequence $2$-clustering problem
\jour Diskretn. Anal. Issled. Oper.
\yr 2016
\vol 23
\issue 2
\pages 21--40
\jour J. Appl. Industr. Math.
\yr 2016
\vol 10
\issue 2
\pages 209--219

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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. 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  mathnet  crossref  crossref  mathscinet  isi  elib
    2. 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
    3. 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  mathnet  crossref  crossref  isi  elib
    4. 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  crossref  mathscinet  isi  scopus
    5. A. V. Kel'manov, V. I. Khandeev, A. V. Panasenko, “Exact Algorithms of Search For a Cluster of the Largest Size in Two Integer 2-Clustering Problems”, Numer. Anal. Appl., 12:2 (2019), 105–115  mathnet  crossref  mathscinet  isi  scopus
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