Online uniformly inserting points on the sphere
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 targ...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI
2018
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| Subjects: | |
| Online Access: | https://eprints.nottingham.ac.uk/55649/ |
| _version_ | 1848799197456760832 |
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| author | Zhou, Rong Chen, Chun Sun, Liqun Lau, Francis Poon, Sheung-Hung Zhang, Yong |
| author_facet | Zhou, Rong Chen, Chun Sun, Liqun Lau, Francis Poon, Sheung-Hung Zhang, Yong |
| author_sort | Zhou, Rong |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:31:50Z |
| format | Article |
| id | nottingham-55649 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:31:50Z |
| publishDate | 2018 |
| publisher | MDPI |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-556492018-12-05T10:43:59Z https://eprints.nottingham.ac.uk/55649/ Online uniformly inserting points on the sphere Zhou, Rong Chen, Chun Sun, Liqun Lau, Francis Poon, Sheung-Hung Zhang, Yong 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. MDPI 2018-10-16 Article PeerReviewed application/pdf en cc_by https://eprints.nottingham.ac.uk/55649/1/algorithms-11-00156.pdf Zhou, Rong, Chen, Chun, Sun, Liqun, Lau, Francis, Poon, Sheung-Hung and Zhang, Yong (2018) Online uniformly inserting points on the sphere. Algorithms, 11 (10). 156/1-156/9. ISSN 1999-4893 online algorithms; uniform insertion; gap ratio https://www.mdpi.com/1999-4893/11/10/156 doi:10.3390/a11100156 doi:10.3390/a11100156 |
| spellingShingle | online algorithms; uniform insertion; gap ratio Zhou, Rong Chen, Chun Sun, Liqun Lau, Francis Poon, Sheung-Hung Zhang, Yong Online uniformly inserting points on the sphere |
| title | Online uniformly inserting points on the sphere |
| title_full | Online uniformly inserting points on the sphere |
| title_fullStr | Online uniformly inserting points on the sphere |
| title_full_unstemmed | Online uniformly inserting points on the sphere |
| title_short | Online uniformly inserting points on the sphere |
| title_sort | online uniformly inserting points on the sphere |
| topic | online algorithms; uniform insertion; gap ratio |
| url | https://eprints.nottingham.ac.uk/55649/ https://eprints.nottingham.ac.uk/55649/ https://eprints.nottingham.ac.uk/55649/ |