@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",
}