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# Locally Private k-Means in One Round

*Proceedings of the 38th International Conference on Machine Learning*, PMLR 139:1441-1451, 2021.

#### Abstract

We provide an approximation algorithm for k-means clustering in the \emph{one-round} (aka \emph{non-interactive}) local model of differential privacy (DP). Our algorithm achieves an approximation ratio arbitrarily close to the best \emph{non private} approximation algorithm, improving upon previously known algorithms that only guarantee large (constant) approximation ratios. Furthermore, ours is the first constant-factor approximation algorithm for k-means that requires only \emph{one} round of communication in the local DP model, positively resolving an open question of Stemmer (SODA 2020). Our algorithmic framework is quite flexible; we demonstrate this by showing that it also yields a similar near-optimal approximation algorithm in the (one-round) shuffle DP model.