Abstract. 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( −1 kz) 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 2 ) memory for a variation motivated by anonymity considerations in which each cluster must contain at least a certain number of input points.
Our construction for universal outliers is somewhat similar conceptually to REF , where a streaming algorithm for k-center clustering with outliers is presented.
Streaming Algorithms for k-Center Clustering with Outliers and with Anonymity
APPROX-RANDOM
Computer Science