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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2019, Volume 59, Number 9, Pages 1617–1625
DOI: https://doi.org/10.1134/S0044466919090114 (Mi zvmmf10959) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Polynomial-time solvability of the one-dimensional case of an NP-hard clustering problem

A. V. Kel'manovab, V. I. Khandeevab

a Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
b Novosibirsk State University, Novosibirsk, 630090 Russia
Citations (1)
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DOI: https://doi.org/10.1134/S0044466919090114
Abstract: We consider the problem of partitioning a finite set of points in Euclidean space into clusters so as to minimize the sum, over all clusters, of the intracluster sums of the squared distances between cluster elements and their centers. The centers of some of the clusters are given as an input, while the centers of the others are determined as centroids (geometric centers). It is known that, in the general case, this problem is strongly NP-hard. We prove constructively that the one-dimensional case of this problem is solvable in polynomial time.
Key words: Euclidean space, clustering, partitioning, minimum sum-of-squares, strongly NP-hard problem, one-dimensional case, polynomial-time solvability.
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
The research presented in Sections 2 and 3 was supported by the Russian Foundation for Basic Research (project nos. 19-01-00308 and 18-31-00398); the research presented in the other sections was supported by the Basic Research Program of the Russian Academy of Sciences (project no. 0314-2019-0015).
Received: 03.04.2019
Revised: 03.04.2019
Accepted: 15.05.2019
English version:
Computational Mathematics and Mathematical Physics, 2019, Volume 59, Issue 9, Pages 1553–1561
DOI: https://doi.org/10.1134/S0965542519090112
Bibliographic databases:
Document Type: Article
UDC: 519.72
Language: Russian
Citation: A. V. Kel'manov, V. I. Khandeev, “Polynomial-time solvability of the one-dimensional case of an NP-hard clustering problem”, Zh. Vychisl. Mat. Mat. Fiz., 59:9 (2019), 1617–1625; Comput. Math. Math. Phys., 59:9 (2019), 1553–1561
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    1. Vladimir Khandeev, Sergey Neshchadim, Lecture Notes in Computer Science, 13078, Optimization and Applications, 2021, 231  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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