Problem
Research questions and friction points this paper is trying to address.
Euclidean Diameter
Dynamic Streams
Space Complexity
A Near-Optimal Space Lower Bound for Euclidean Diameter Estimation in Dynamic Streams
🤖 AI Summary
本文研究了动态流模型中欧几里得空间点集直径估计的空间复杂性问题，证明了任何能够c-近似估计n个向量直径的算法需要至少n^Ω(1/c^2)的空间。
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
space complexity
diameter estimation
dynamic streaming model
Euclidean space
lower bound
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