A simple approximation algorithm for the diameter of a set of points in an Euclidean plane

被引：1

作者：

Hong, Jieying ^{[1
]}

Wang, Zhipeng ^{[2
]}

Niu, Wei ^{[2
,3
]}

机构：

[1] ESSEC Business Sch, ESSEC Asia Pacific, Singapore, Singapore

[2] Beihang Univ, Ecole Cent Pekin, Beijing, Peoples R China

[3] Beihang Univ, Beijing Adv Innovat Ctr Big Data & Brain Comp, Beijing, Peoples R China

来源：

PLOS ONE | 2019年 / 14卷 / 02期

基金：

中国国家自然科学基金;

关键词：

HYPERSPHERE;

D O I：

10.1371/journal.pone.0211201

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Approximation algorithms with linear complexities are required in the treatments of big data, however, present algorithms cannot output the diameter of a set of points with arbitrary accuracy and near-linear complexity. By introducing the partition technique, we introduce a very simple approximation algorithm with arbitrary accuracy epsilon and a complexity of O(N + epsilon(-1) log epsilon(-1)) for the cases that all points are located in an Euclidean plane. The error bounds are proved strictly, and are verified by numerical tests. This complexity is better than existing algorithms, and the present algorithm is also very simple to be implemented in applications.

引用

页数：13

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