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arXiv · 2505.16720

Streaming Diameter of High-Dimensional Points

Magnús M. Halldórsson·Nicolaos Matsakis·Pavel Veselý
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Abstract

We improve the space bound for streaming approximation of Diameter but also of Farthest Neighbor queries, Minimum Enclosing Ball and its Coreset, in high-dimensional Euclidean spaces. In particular, our deterministic streaming algorithms store $\mathcal{O}(\varepsilon^{-2}\log(\frac{1}{\varepsilon}))$ points. This improves by a factor of $\varepsilon^{-1}$ the previous space bound of Agarwal and Sharathkumar (SODA 2010), while offering a simpler and more complete argument. We also show that storing $\Omega(\varepsilon^{-1})$ points is necessary for a $(\sqrt{2}+\varepsilon)$-approximation of Farthest Pair or Farthest Neighbor queries.

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Magnús M. Halldórsson, Nicolaos Matsakis, Pavel Veselý. 2025-05-22. Streaming Diameter of High-Dimensional Points. https://arxiv.org/abs/2505.16720

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