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arXiv · 1610.08543

An efficient approximation for point-set diameter in higher dimensions

Mahdi Imanparast·Seyed Naser Hashemi·Ali Mohades
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Abstract

In this paper, we study the problem of computing the diameter of a set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+\varepsilon)$-approximation algorithm with $O(n+ 1/\varepsilon^{d-1})$ time and $O(n)$ space, where $0 < \varepsilon\leqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(\varepsilon))$-approximation algorithm with $O(n+ 1/\varepsilon^{\frac{2d}{3}-\frac{1}{3}})$ running time. These results provide some improvements in comparison with existing algorithms in terms of simplicity and data structure.

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Mahdi Imanparast, Seyed Naser Hashemi, Ali Mohades. 2019-05-07. An efficient approximation for point-set diameter in higher dimensions. https://arxiv.org/abs/1610.08543

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