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arXiv · 1004.2968

Clustering with diversity

Jian Li·Ke Yi·Qin Zhang
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Abstract

We consider the {\em 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 $\ell$ points, all of which have distinct colors. We give a 2-approximation to this problem for any $\ell$ when the objective is to minimize the maximum radius of any cluster. We show that the approximation ratio is optimal unless $\mathbf{P=NP}$, 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.

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Jian Li, Ke Yi, Qin Zhang. 2010-04-21. Clustering with diversity. https://arxiv.org/abs/1004.2968

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