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.
CITATION STYLE
Kel’manov, A., & Motkova, A. (2016). A fully polynomial-time approximation scheme for a special case of a balanced 2-clustering problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9869 LNCS, pp. 182–192). Springer Verlag. https://doi.org/10.1007/978-3-319-44914-2_15
Mendeley helps you to discover research relevant for your work.