Streaming Algorithms for k-Center Clustering with Outliers and with Anonymity

Clustering is a common problem in the analysis of large data sets. Streaming algorithms, which make a single pass over the data set using small working memory and produce a clustering comparable in cost to the optimal offline solution, are especially useful. We develop the first streaming algorithms achieving a constant-factor approximation to the cluster radius for two variations of the k-center clustering problem. We give a streaming (4 + )-approximation algorithm using O( −1kz) memory for the problem with outliers, in which the clustering is allowed to drop up to z of the input points; previous work used a random sampling approach which yields only a bicriteria approximation. We also give a streaming (6+ )approximation algorithm using O( −1 ln( −1)k + k) memory for a variation motivated by anonymity considerations in which each cluster must contain at least a certain number of input points.