Clustering with Diversity

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 points, all of which have distinct colors. We give a 2-approximation to this problem for any 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. Key words: Approximation algorithm, k-center, k-anonymity, l-diversity

• Type: Conference
• Year: 2010
• Where: ICALP
• Authors: Jian Li, Ke Yi, Qin Zhang
• Keywords: Distinct Colors, Diversity Problem, ICALP 2010, Metric Space, Programming Languages