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Online Uniformly Inserting Points on the Sphere

Research Center for High Performance Computing, Joint Engineering Research Center for Health Big Data Intelligent Analysis Technology, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, 1068 Xueyuan Avenue, Shenzhen University Town, Shenzhen 518055, China
University of Chinese Academy of Sciences, 19(A) Yuquan Road, Shijingshan District, Beijing 100049, China
Department of Computer Science, The University of Hong Kong, Pokfulam, Hong Kong, China
School of Computer Science, University of Nottingham Ningbo China, 199 Taikang East Road, Ningbo 315100, China
Author to whom correspondence should be addressed.
This paper is an extended version of our paper published in the 11th International Conference and Workshops on Algorithms and Computation (WALCOM 2017).
Algorithms 2018, 11(10), 156;
Received: 11 August 2018 / Revised: 25 September 2018 / Accepted: 11 October 2018 / Published: 16 October 2018
PDF [570 KB, uploaded 16 October 2018]


Uniformly inserting points on the sphere has been found useful in many scientific and engineering fields. Different from the offline version where the number of points is known in advance, we consider the online version of this problem. The requests for point insertion arrive one by one and the target is to insert points as uniformly as possible. To measure the uniformity we use gap ratio which is defined as the ratio of the maximal gap to the minimal gap of two arbitrary inserted points. We propose a two-phase online insertion strategy with gap ratio of at most 3.69 . Moreover, the lower bound of the gap ratio is proved to be at least 1.78 . View Full-Text
Keywords: online algorithms; uniform insertion; gap ratio online algorithms; uniform insertion; gap ratio

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Zhou, R.; Chen, C.; Sun, L.; Lau, F.C.M.; Poon, S.-H.; Zhang, Y. Online Uniformly Inserting Points on the Sphere. Algorithms 2018, 11, 156.

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