On the Complexity of Some Quadratic Euclidean Partition Problems into Balanced Clusters

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On the Complexity of Some Quadratic Euclidean Partition Problems into Balanced Clusters. / Kel’manov, Alexander; Khandeev, Vladimir ; Pyatkin, Artem.

Optimization and Applications - 10th International Conference, OPTIMA 2019, Revised Selected Papers. ed. / Milojica Jaćimović; Michael Khachay; Vlasta Malkova; Mikhail Posypkin. Springer Gabler, 2020. p. 127-136 (Communications in Computer and Information Science; Vol. 1145 CCIS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

Harvard

Kel’manov, A, Khandeev, V & Pyatkin, A 2020, On the Complexity of Some Quadratic Euclidean Partition Problems into Balanced Clusters. in M Jaćimović, M Khachay, V Malkova & M Posypkin (eds), Optimization and Applications - 10th International Conference, OPTIMA 2019, Revised Selected Papers. Communications in Computer and Information Science, vol. 1145 CCIS, Springer Gabler, pp. 127-136, 10th International Conference on Optimization and Applications, OPTIMA 2019, Petrovac, Montenegro, 30.09.2019. https://doi.org/10.1007/978-3-030-38603-0_10

APA

Kel’manov, A., Khandeev, V., & Pyatkin, A. (2020). On the Complexity of Some Quadratic Euclidean Partition Problems into Balanced Clusters. In M. Jaćimović, M. Khachay, V. Malkova, & M. Posypkin (Eds.), Optimization and Applications - 10th International Conference, OPTIMA 2019, Revised Selected Papers (pp. 127-136). (Communications in Computer and Information Science; Vol. 1145 CCIS). Springer Gabler. https://doi.org/10.1007/978-3-030-38603-0_10

Vancouver

Kel’manov A, Khandeev V , Pyatkin A. On the Complexity of Some Quadratic Euclidean Partition Problems into Balanced Clusters. In Jaćimović M, Khachay M, Malkova V, Posypkin M, editors, Optimization and Applications - 10th International Conference, OPTIMA 2019, Revised Selected Papers. Springer Gabler. 2020. p. 127-136. (Communications in Computer and Information Science). doi: 10.1007/978-3-030-38603-0_10

Author

Kel’manov, Alexander ; Khandeev, Vladimir ; Pyatkin, Artem. / On the Complexity of Some Quadratic Euclidean Partition Problems into Balanced Clusters. Optimization and Applications - 10th International Conference, OPTIMA 2019, Revised Selected Papers. editor / Milojica Jaćimović ; Michael Khachay ; Vlasta Malkova ; Mikhail Posypkin. Springer Gabler, 2020. pp. 127-136 (Communications in Computer and Information Science).

BibTeX

@inproceedings{7ae1328e04194e76af54a268666aebfc,

title = "On the Complexity of Some Quadratic Euclidean Partition Problems into Balanced Clusters",

abstract = "We consider three problems of partitioning a finite set of N points in the d-dimensional Euclidean space into two clusters balancing the value of (1) the normalized by a cluster size sum of squared deviations from the mean, (2) the sum of squared deviations from the mean, and (3) the size-weighted sum of squared deviations from the mean. We have proved the NP-completeness of all these problems.",

keywords = "Balanced partition, Euclidean space, Normalized by the cluster size, NP-completeness, Quadratic variance, Sized-weighted",

author = "Alexander Kel{\textquoteright}manov and Vladimir Khandeev and Artem Pyatkin",

note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2020. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.; 10th International Conference on Optimization and Applications, OPTIMA 2019 ; Conference date: 30-09-2019 Through 04-10-2019",

year = "2020",

month = jan,

day = "1",

doi = "10.1007/978-3-030-38603-0_10",

language = "English",

isbn = "9783030386023",

series = "Communications in Computer and Information Science",

publisher = "Springer Gabler",

pages = "127--136",

editor = "Milojica Ja{\'c}imovi{\'c} and Michael Khachay and Vlasta Malkova and Mikhail Posypkin",

booktitle = "Optimization and Applications - 10th International Conference, OPTIMA 2019, Revised Selected Papers",

address = "Germany",

}

RIS

TY - GEN

T1 - On the Complexity of Some Quadratic Euclidean Partition Problems into Balanced Clusters

AU - Kel’manov, Alexander

AU - Khandeev, Vladimir

AU - Pyatkin, Artem

PY - 2020/1/1

Y1 - 2020/1/1

N2 - We consider three problems of partitioning a finite set of N points in the d-dimensional Euclidean space into two clusters balancing the value of (1) the normalized by a cluster size sum of squared deviations from the mean, (2) the sum of squared deviations from the mean, and (3) the size-weighted sum of squared deviations from the mean. We have proved the NP-completeness of all these problems.

AB - We consider three problems of partitioning a finite set of N points in the d-dimensional Euclidean space into two clusters balancing the value of (1) the normalized by a cluster size sum of squared deviations from the mean, (2) the sum of squared deviations from the mean, and (3) the size-weighted sum of squared deviations from the mean. We have proved the NP-completeness of all these problems.

KW - Balanced partition

KW - Euclidean space

KW - Normalized by the cluster size

KW - NP-completeness

KW - Quadratic variance

KW - Sized-weighted

UR - http://www.scopus.com/inward/record.url?scp=85078452712&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-38603-0_10

DO - 10.1007/978-3-030-38603-0_10

M3 - Conference contribution

AN - SCOPUS:85078452712

SN - 9783030386023

T3 - Communications in Computer and Information Science

SP - 127

EP - 136

BT - Optimization and Applications - 10th International Conference, OPTIMA 2019, Revised Selected Papers

A2 - Jaćimović, Milojica

A2 - Khachay, Michael

A2 - Malkova, Vlasta

A2 - Posypkin, Mikhail

PB - Springer Gabler

T2 - 10th International Conference on Optimization and Applications, OPTIMA 2019

Y2 - 30 September 2019 through 4 October 2019

ER -

ID: 23265235