Locally Private k-Means in One Round

TL;DR

This paper introduces a one-round local differential privacy algorithm for k-means clustering that achieves near-optimal approximation ratios, resolving an open problem and extending to the shuffle DP model.

Contribution

It presents the first constant-factor approximation algorithm for k-means in the one-round local DP model, improving previous results and demonstrating flexibility in the shuffle DP model.

Findings

Achieves approximation ratios close to non-private algorithms.

First one-round constant-factor approximation for k-means in local DP.

Extends framework to shuffle DP model.

Abstract

We provide an approximation algorithm for k-means clustering in the one-round (aka non-interactive) local model of differential privacy (DP). This algorithm achieves an approximation ratio arbitrarily close to the best non private approximation algorithm, improving upon previously known algorithms that only guarantee large (constant) approximation ratios. Furthermore, this is the first constant-factor approximation algorithm for k-means that requires only 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.