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arXiv · 2608.27896

Online Differentially Private Consistent Clustering

Edith Cohen·Vadym Doroshenko·Badih Ghazi·Pritish Kamath·Alexander Knop·Ravi Kumar·Ethan Leeman·Pasin Manurangsi·Adam Sealfon·Marika Swanberg
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Abstract

We study differentially private (DP) $k$-means and $k$-median clustering in the online streaming setting. In this model, points arrive sequentially, and at each time step, we need to output a set of $k$ centers that optimizes the clustering objective for all points seen so far. We give a generic reduction that transforms the (sensitive) input stream into a private stream, which is a semi-coreset of the input stream. This implies that any (non-private) online clustering algorithm, run as a post-processing step, can achieve good utility for the original clustering objective. Our algorithm matches or improves upon the approximation ratio, space usage, and running time of existing algorithms [Epasto et al., 2026, Dupré la Tour et al., 2024]. A key aspect of our reduction is that it inherits desirable properties of the underlying non-private clustering algorithm, such as consistency [Lattanzi and Vassilvitskii, 2017]--a property not satisfied by previous DP algorithms.

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Edith Cohen, Vadym Doroshenko, Badih Ghazi, Pritish Kamath, Alexander Knop, Ravi Kumar, Ethan Leeman, Pasin Manurangsi, Adam Sealfon, Marika Swanberg. 2026-08-28. Online Differentially Private Consistent Clustering. https://arxiv.org/abs/2608.27896

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