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NP-hardness of Some Max-Min Clustering Problems

  • Alexander Kel’manov
  • Vladimir Khandeev
  • Artem Pyatkin
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 974)

Abstract

We consider some consimilar problems of searching for disjoint clusters in the finite set of points in Euclidean space. The goal is to maximize the minimum subset size so that the value of each intracluster quadratic variation would not exceed a given constant. We prove that all considered problems are NP-hard even on a line.

Keywords

Euclidean space Clustering Max-Min problem NP-hardness Quadratic variation 

Notes

Acknowledgments

The study presented was supported by the Russian Science Foundation, project 16-11-10041.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

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

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