Clustering with diversity

  • Authors:
  • Jian Li;Ke Yi;Qin Zhang

  • Affiliations:
  • University of Maryland, College Park, MD;Hong Kong University of Science and Technology, Hong Kong, China;Hong Kong University of Science and Technology, Hong Kong, China

  • Venue:
  • ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
  • Year:
  • 2010

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Abstract

We consider the clustering with diversity problem: given a set of colored points in a metric space, partition them into clusters such that each cluster has at least l points, all of which have distinct colors. We give a 2-approximation to this problem for any l when the objective is to minimize the maximum radius of any cluster. We show that the approximation ratio is optimal unless P = NP, by providing a matching lower bound. Several extensions to our algorithm have also been developed for handling outliers. This problem is mainly motivated by applications in privacy-preserving data publication.