Differentially Private Clustering: Tight Approximation Ratios
This work addresses privacy-preserving data analysis for clustering tasks, offering near-optimal solutions with practical efficiency, though it is incremental in building upon existing differential privacy frameworks.
The paper tackles the problem of differentially private clustering for Euclidean DensestBall, 1-Cluster, k-means, and k-median, achieving approximation ratios nearly matching non-private algorithms with small additive errors, improving upon prior constant-factor approximations.
We study the task of differentially private clustering. For several basic clustering problems, including Euclidean DensestBall, 1-Cluster, k-means, and k-median, we give efficient differentially private algorithms that achieve essentially the same approximation ratios as those that can be obtained by any non-private algorithm, while incurring only small additive errors. This improves upon existing efficient algorithms that only achieve some large constant approximation factors. Our results also imply an improved algorithm for the Sample and Aggregate privacy framework. Furthermore, we show that one of the tools used in our 1-Cluster algorithm can be employed to get a faster quantum algorithm for ClosestPair in a moderate number of dimensions.