Near-Linear Time Approximation Schemes for Clustering in Doubling Metrics

12/20/2018

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by   Vincent Cohen-Addad, et al.

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We consider the classic Facility Location, k-Median, and k-Means problems in metric spaces of doubling dimension d. We give nearly-linear time approximation schemes for each problem. The complexity of our algorithms is 2^(d/ε)^O(d) n ^4 n + 2^O(d) n ^9 n, making a significant improvement over the state-of-the-art algorithm which runs in time n^(d/ε)^O(d).