@inproceedings{9bfba5f063ed4bab953da0ba28ac3912,
title = "A fully polynomial-time approximation scheme for a special case of a balanced 2-clustering problem",
abstract = "We consider the strongly NP-hard problem of partitioning a set of Euclidean points into two clusters so as to minimize the sum (over both clusters) of the weighted sum of the squared intracluster distances from the elements of the clusters to their centers. The weights of sums are the cardinalities of the clusters. The center of one of the clusters is given as input, while the center of the other cluster is unknown and determined as the geometric center (centroid), i.e. the average value over all points in the cluster. We analyze the variant of the problem with cardinality constraints. We present an approximation algorithm for the problem and prove that it is a fully polynomial-time approximation scheme when the space dimension is bounded by a constant.",
keywords = "Euclidian space, Fixed dimension, FPTAS, NP-hardness",
author = "Alexander Kel{\textquoteright}manov and Anna Motkova",
year = "2016",
doi = "10.1007/978-3-319-44914-2_15",
language = "English",
isbn = "9783319449135",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer-Verlag GmbH and Co. KG",
pages = "182--192",
editor = "Michael Khachay and Panos Pardalos and Yury Kochetov and Vladimir Beresnev and Evgeni Nurminski",
booktitle = "Discrete Optimization and Operations Research - 9th International Conference, DOOR 2016, Proceedings",
address = "Germany",
note = "9th International Conference on Discrete Optimization and Operations Research, DOOR 2016 ; Conference date: 19-09-2016 Through 23-09-2016",
}