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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 1, Pages 151–158 (Mi zvmmf11025)  

Complexity of some problems of quadratic partitioning of a finite set of points in Euclidean space into balanced clusters

A. V. Kel'manovab, A. V. Pyatkinab, V. I. Khandeevab

a Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
b Novosibirsk State University, Novosibirsk, 630090 Russia

Abstract: We consider three related problems of partitioning an $N$-element set of points in $d$-dimensional Euclidean space into two clusters balancing the value of the intracluster quadratic variance normalized by the cluster size in the first problem, the intracluster quadratic variance in the second problem, and the size-weighted intracluster variance in the third problem. The NP-completeness of all these problems is proved.

Key words: Euclidean space, balanced partition, quadratic variance, variance normalized by the cluster size, size-weighted variance, NP-completeness.

Funding Agency Grant Number
Russian Foundation for Basic Research 19-01-00308
18-31-00398
Russian Academy of Sciences - Federal Agency for Scientific Organizations 0314-2019-0015
0314-2019-0014
Ministry of Science and Higher Education of the Russian Federation 5-100
This work was supported by the Russian Foundation for Basic Research (project nos. 19-01-00308 and 18-31-00398), by Basic Research Programs of the Russian Academy of Sciences (project nos. 0314-2019-0015 and 0314-2019-0014), and by the Top-5-100 Program of the Ministry of Education and Science of the Russian Federation.


DOI: https://doi.org/10.31857/S0044466919110061


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:1, 163–170

Bibliographic databases:

UDC: 519.72
Received: 20.05.2019
Revised: 20.05.2019
Accepted:18.09.2019

Citation: A. V. Kel'manov, A. V. Pyatkin, V. I. Khandeev, “Complexity of some problems of quadratic partitioning of a finite set of points in Euclidean space into balanced clusters”, Zh. Vychisl. Mat. Mat. Fiz., 60:1 (2020), 151–158; Comput. Math. Math. Phys., 60:1 (2020), 163–170

Citation in format AMSBIB
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\paper Complexity of some problems of quadratic partitioning of a finite set of points in Euclidean space into balanced clusters
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2020
\vol 60
\issue 1
\pages 151--158
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\crossref{https://doi.org/10.31857/S0044466919110061}
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\transl
\jour Comput. Math. Math. Phys.
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\pages 163--170
\crossref{https://doi.org/10.1134/S096554251911006X}
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