Standard

On the Complexity of Some Problems of Searching for a Family of Disjoint Clusters. / Kel’manov, A. V.; Pyatkin, A. V.; Khandeev, V. I.

In: Doklady Mathematics, Vol. 99, No. 1, 01.01.2019, p. 52-56.

Research output: Contribution to journal › Article › peer-review

Harvard

Kel’manov, AV, Pyatkin, AV & Khandeev, VI 2019, 'On the Complexity of Some Problems of Searching for a Family of Disjoint Clusters', Doklady Mathematics, vol. 99, no. 1, pp. 52-56. https://doi.org/10.1134/S1064562419010162

APA

Kel’manov, A. V., Pyatkin, A. V., & Khandeev, V. I. (2019). On the Complexity of Some Problems of Searching for a Family of Disjoint Clusters. Doklady Mathematics, 99(1), 52-56. https://doi.org/10.1134/S1064562419010162

Vancouver

Kel’manov AV, Pyatkin AV, Khandeev VI. On the Complexity of Some Problems of Searching for a Family of Disjoint Clusters. Doklady Mathematics. 2019 Jan 1;99(1):52-56. doi: 10.1134/S1064562419010162

Author

Kel’manov, A. V. ; Pyatkin, A. V. ; Khandeev, V. I. / On the Complexity of Some Problems of Searching for a Family of Disjoint Clusters. In: Doklady Mathematics. 2019 ; Vol. 99, No. 1. pp. 52-56.

BibTeX

@article{b36cfe1459cf430b8948abca71f3192a,
title = "On the Complexity of Some Problems of Searching for a Family of Disjoint Clusters",
abstract = "Abstract: Two consimilar problems of searching for a family of disjoint subsets (clusters) in a finite set of points of Euclidean space are considered. In these problems, the task is to maximize the minimum cluster size so that the value of each intercluster quadratic variation does not exceed a given fraction (constant) of the total quadratic variation of the points of the input set with respect to its centroid. Both problems are proved to be NP-hard even on a line.",
keywords = "ALGORITHM, 2-CENTER",
author = "Kel{\textquoteright}manov, {A. V.} and Pyatkin, {A. V.} and Khandeev, {V. I.}",
year = "2019",
month = jan,
day = "1",
doi = "10.1134/S1064562419010162",
language = "English",
volume = "99",
pages = "52--56",
journal = "Doklady Mathematics",
issn = "1064-5624",
publisher = "Maik Nauka-Interperiodica Publishing",
number = "1",

}

RIS

TY - JOUR

T1 - On the Complexity of Some Problems of Searching for a Family of Disjoint Clusters

AU - Kel’manov, A. V.

AU - Pyatkin, A. V.

AU - Khandeev, V. I.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Abstract: Two consimilar problems of searching for a family of disjoint subsets (clusters) in a finite set of points of Euclidean space are considered. In these problems, the task is to maximize the minimum cluster size so that the value of each intercluster quadratic variation does not exceed a given fraction (constant) of the total quadratic variation of the points of the input set with respect to its centroid. Both problems are proved to be NP-hard even on a line.

AB - Abstract: Two consimilar problems of searching for a family of disjoint subsets (clusters) in a finite set of points of Euclidean space are considered. In these problems, the task is to maximize the minimum cluster size so that the value of each intercluster quadratic variation does not exceed a given fraction (constant) of the total quadratic variation of the points of the input set with respect to its centroid. Both problems are proved to be NP-hard even on a line.

KW - ALGORITHM

KW - 2-CENTER

UR - http://www.scopus.com/inward/record.url?scp=85065864468&partnerID=8YFLogxK

U2 - 10.1134/S1064562419010162

DO - 10.1134/S1064562419010162

M3 - Article

AN - SCOPUS:85065864468

VL - 99

SP - 52

EP - 56

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - 1

ER -

ID: 20050501