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Diskretn. Anal. Issled. Oper., 2016, Volume 23, Issue 3, Pages 21–34 (Mi da850)  

This article is cited in 7 scientific papers (total in 7 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

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


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English version:
Journal of Applied and Industrial Mathematics, 2016, 10:3, 349–355

Bibliographic databases:

UDC: 519.16+519.85
Received: 25.05.2016

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
\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
\jour J. Appl. Industr. Math.
\yr 2016
\vol 10
\issue 3
\pages 349--355

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    This publication is cited in the following articles:
    1. A. V. Kel'manov, A. V. Motkova, V. V. Shenmaier, “Approximation scheme for the problem of weighted 2-partitioning with a fixed center of one cluster”, Proc. Steklov Inst. Math. (Suppl.), 303, suppl. 1 (2018), 136–145  mathnet  crossref  crossref  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. 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
    4. 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
    5. A. Kel'manov, A. Motkova, V. Shenmaier, “An approximation scheme for a weighted two-cluster partition problem”, 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, 323–333  crossref  isi  scopus
    6. 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
    7. A. Panasenko, “A PTAS for one cardinality-weighted 2-clustering problem”, Mathematical Optimization Theory and Operations Research, Lecture Notes in Computer Science, 11548, ed. M. Khachay, Y. Kochetov, P. Pardalos, Springer, 2019, 581–592  crossref  zmath  isi  scopus
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