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 /\varepsilon) ^{O(d) } n \log^4 n + 2^{O(d)} n \log^9 n, making a significant improvement over the state-of-the-art algorithm which runs in time n^{(d/\varepsilon)^{O(d)}}.
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^{( \log(1 /\varepsilon) /\varepsilon)^{O(d^2) } n \log^4 n + 2^{O(d)} n \log^9 n, making a significant improvement over the state-of-the-art algorithm which runs in time n^{(d/\varepsilon)^{O(d)}}.
R
d
\log(1
R
^{O(d)
/\varepsilon)^{O(d^2)