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A Fully Polynomial-Time Approximation Scheme for a Special Case of a Balanced 2-Clustering Problem

  • Alexander Kel’manovEmail author
  • Anna MotkovaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9869)

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

NP-hardness Euclidian space Fixed dimension FPTAS 

Notes

Acknowledgments

This work was supported by the RFBR, projects 15-01-00462, 16-31-00186 and 16-07-00168.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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