Fast and Robust Approximation of Smallest Enclosing Balls in Arbitrary Dimensions
Article first published online: 19 AUG 2013
© 2013 The Author(s) Computer Graphics Forum © 2013 The Eurographics Association and John Wiley & Sons Ltd.
Computer Graphics Forum
Volume 32, Issue 5, pages 93–101, August 2013
How to Cite
Larsson, T. and Källberg, L. (2013), Fast and Robust Approximation of Smallest Enclosing Balls in Arbitrary Dimensions. Computer Graphics Forum, 32: 93–101. doi: 10.1111/cgf.12176
- Issue published online: 19 AUG 2013
- Article first published online: 19 AUG 2013
- Computer Graphics [I.3.5]: Computational Geometry and Object Modeling—Geometric algorithms, languages, and systems;
- Analysis of algorithms and problem complexity [F.2.2]: Nonnumerical Algorithms and Problems—Geometrical problems and computations
In this paper, an algorithm is introduced that computes an arbitrarily fine approximation of the smallest enclosing ball of a point set in any dimension. This operation is important in, for example, classification, clustering, and data mining. The algorithm is very simple to implement, gives reliable results, and gracefully handles large problem instances in low and high dimensions, as confirmed by both theoretical arguments and empirical evaluation. For example, using a CPU with eight cores, it takes less than two seconds to compute a 1.001-approximation of the smallest enclosing ball of one million points uniformly distributed in a hypercube in dimension 200. Furthermore, the presented approach extends to a more general class of input objects, such as ball sets.