The main contribution is giving an essentially matching lower bound on the space complexity of diameter estimation for a set of points in Euclidean space in the dynamic (turnstile) streaming model.
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 $n^{\tilde{\Omega}(1/c^2)}$ space.
We show that an almost-everywhere upper bound $b\geq 1$ for the Hausdorff dimension of visible parts of all compact planar sets implies the upper bound $d-2+b$ for visible parts of all compact sets $K$ in $\mathbb{R}^d$, $d\geq3$. Inserting the sharp planar bound $b=3/2$ of Orponen and Rutar \cite{OrponenRutar2026} giv...
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Trevor Vaughn· 0 citations
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