For Euclidean k-center with k=n^c, the paper gives an O(1)-approximation in near-linear time by building small coresets via a new efficient consistent hashing.
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Faster Approximation Algorithms for k-Center via Data Reduction
For Euclidean k-center with k=n^c, the paper gives an O(1)-approximation in near-linear time by building small coresets via a new efficient consistent hashing.