Near-linear time approximations schemes for clustering in doubling metrics

Abstract

We consider the classic Facility Location, k-Median, and k-Means problems in metric spaces of constant doubling dimension. We give the first nearly linear-Time approximation schemes for each problem, making a significant improvement over the state-of-The-Art algorithms.

Moreover, we show how to extend the techniques used to get the first efficient approximation schemes for the problems of prize-collecting k-Medians and k-Means, and efficient bicriteria approximation schemes for k-Medians with outliers, k-Means with outliers and k-Center.

Keywords

• clustering
• doubling metrics