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arXiv · 2611.07678

Adversarially Robust Streaming Algorithms for $(k, z)$-Clustering

Chengzhi Guo·Shaofeng H. C. Jiang·Robert Krauthgamer·David P. Woodruff·Shenghao Xie·Samson Zhou
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Abstract

We design adversarially robust algorithms for dynamic geometric streams that $(1 + ε)$-approximate $k$-Median and $k$-Means in Euclidean space $\mathbb{R}^d$, using $\tilde{O}(kd \mathrm{poly}(ε^{-1}))$ space. This result significantly improves a recent $O(d\log n)$-approximation for $k$-Median [Gribelyuk, Lin, Woodruff, Yu, and Zhou, FOCS 2026], and is furthermore the first algorithm whose space is linear in $kd$, even in the oblivious (non-adaptive) setting. We develop several new techniques which may be of independent interest, including a new data-oblivious Euclidean primitive called hierarchical Lipschitz assignment, a robust dimensionality reduction for clustering, and a robust streaming algorithm for inner-product queries.

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Chengzhi Guo, Shaofeng H. C. Jiang, Robert Krauthgamer, David P. Woodruff, Shenghao Xie, Samson Zhou. 2026-11-05. Adversarially Robust Streaming Algorithms for $(k, z)$-Clustering. https://arxiv.org/abs/2611.07678

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