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Efficient Speed-Up of the Smallest Enclosing Circle Algorithm
Volume 33, Issue 3 (2022), pp. 623–633
Pub. online: 18 March 2022      Type: Research Article      Open accessOpen Access
Received
1 February 2021
Accepted
1 February 2022
Published
18 March 2022

Abstract

The smallest enclosing circle is a well-known problem. In this paper, we propose modifications to speed-up the existing Weltzl’s algorithm. We perform the preprocessing to reduce as many input points as possible. The reduction step has lower computational complexity than the Weltzl’s algorithm and thus speed-ups its computation. Next, we propose some changes to Weltzl’s algorithm. In the end are summarized results, that show the speed-up for ${10^{6}}$ input points up to 100 times compared to the original Weltzl’s algorithm. Even more, the proposed algorithm is capable to process significantly larger data sets than the standard Weltzl’s algorithm.

References

 
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Biographies

Smolik Michal
smolik@kiv.zcu.cz

M. Smolik received the PhD degree in software engineering from the University of West Bohemia, Czech Republic, in 2020. He currently holds the position of researcher at the Department of Computer Graphics at the University of West Bohemia. His research areas are meshless methods for approximation and interpolation, specifically Radial basis functions. He works in the area of vector fields and develops basic algorithms connected with computer graphics.

Skala Vaclav
skala@kiv.zcu.cz

V. Skala is a full professor of computer science at the University of West Bohemia, Plzen, Czech Republic. He received his ING. (equivalent of MSc) degree in 1975 from the Institute of Technology in Plzen and CSc. (equivalent of PhD) degree from the Czech Technical University in Prague, in 1981. In 1996, he became a full professor in computer science. His current research interests are computer graphics and visualization, applied mathematics, especially geometrical algebra, algorithms, and data structures.


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Copyright
© 2022 Vilnius University
Open access article under the CC BY license.

Keywords
smallest enclosing circle space subdivision convex hull speed-up Weltzl’s algorithm

Funding
The research was supported by the University of West Bohemia – Institutional research support No. 1311, and by SGS 2019-016.

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