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arXiv · 2609.19089

A Near-Optimal Space Lower Bound for Euclidean Diameter Estimation in Dynamic Streams

Ashwin Padaki·Krish Singal·Erik Waingarten
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Abstract

We study the space complexity of diameter estimation for a set of points in Euclidean space in the dynamic (turnstile) streaming model. The seminal work of Indyk (SODA 2003) gives a $c$-approximation to the Euclidean diameter of $n$ vectors using $n^{O(1/c^2)}$ space. Our main contribution is giving an essentially matching lower bound. Any dynamic streaming algorithm which can $c$-approximate the diameter of $n$ Euclidean vectors must use $n^{\tildeΩ(1/c^2)}$ space.

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BibTeXRIS

Ashwin Padaki, Krish Singal, Erik Waingarten. 2026-09-16. A Near-Optimal Space Lower Bound for Euclidean Diameter Estimation in Dynamic Streams. https://arxiv.org/abs/2609.19089

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