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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 12, Pages 2169–2178 (Mi zvmmf10812)  

A randomized algorithm for a sequence 2-clustering problem

A. V. Kel'manovab, S. A. Khamidullina, V. I. Khandeeva

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

Abstract: We consider a strongly NP-hard problem of partitioning a finite Euclidean sequence into two clusters of given cardinalities minimizing the sum over both clusters of intracluster sums of squared distances from clusters elements to their centers. The center of one cluster is unknown and is defined as the mean value of all points in the cluster. The center of the other cluster is the origin. Additionally, the difference between the indices of two consequent points from the first cluster is bounded from below and above by some constants. A randomized algorithm that finds an approximation solution of the problem in polynomial time for given values of the relative error and failure probability and for an established parameter value is proposed. The conditions are established under which the algorithm is polynomial and asymptotically exact.

Key words: partitioning, sequence, Euclidean space, minimum sum-of-squared distances, NP-hardness, randomized algorithm, asymptotic accuracy.

Funding Agency Grant Number
Russian Science Foundation 16-11-10041


DOI: https://doi.org/10.31857/S004446690003560-7

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:12, 2078–2085

Bibliographic databases:

UDC: 519.16:519.85
Received: 26.08.2016

Citation: A. V. Kel'manov, S. A. Khamidullin, V. I. Khandeev, “A randomized algorithm for a sequence 2-clustering problem”, Zh. Vychisl. Mat. Mat. Fiz., 58:12 (2018), 2169–2178; Comput. Math. Math. Phys., 58:12 (2018), 2078–2085

Citation in format AMSBIB
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\paper A randomized algorithm for a sequence 2-clustering problem
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\vol 58
\issue 12
\pages 2169--2178
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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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