Near-linear Time Approximation Schemes for Clustering in Doubling Metrics

We consider the classic Facility Location, k -Median, and -Means problems in metric spaces of doubling dimension d . give nearly linear-time approximation schemes for each problem. The complexity our algorithms is Õ(2 (1/?) O(d2) n) , making a significant improvement over state-of-the-art that run time n (d/?) O(d) Moreover, we show how to extend techniques used get first efficient prize-collecting -Median bicriteria with outliers, outliers -Center.