Clustering with Diversity

Jian Li, Ke Yi, Qin Zhang

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.