An O(log log n)-round low-local-space MPC algorithm for Euclidean k-center that outputs k(1+o(1)) centers with O(log* n) approximation.
Goodrich, Nodari Sitchinava, and Qin Zhang
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On Parallel $k$-Center Clustering
An O(log log n)-round low-local-space MPC algorithm for Euclidean k-center that outputs k(1+o(1)) centers with O(log* n) approximation.