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We study the private k-median and k-means clustering problem in d dimensional Euclidean space. By leveraging tree embeddings, we give an efficient and easy to implement algorithm, that is empirically competitive with state of the art non private methods. We prove that our method computes a solution with cost at most O(d^3/2log n)· OPT + O(k d^2 log^2 n / ϵ^2), where ϵ is the privacy guarantee. (The dimension term, d, can be replaced with O(log k) using standard dimension reduction techniques.)arXiv:2206.08646v1 fatcat:7vdh52qezvgtzdsdpz72r64xba