You are required to read and agree to the below before accessing a full-text version of an article in the IDE article repository.

The full-text document you are about to access is subject to national and international copyright laws. In most cases (but not necessarily all) the consequence is that personal use is allowed given that the copyright owner is duly acknowledged and respected. All other use (typically) require an explicit permission (often in writing) by the copyright owner.

For the reports in this repository we specifically note that

  • the use of articles under IEEE copyright is governed by the IEEE copyright policy (available at http://www.ieee.org/web/publications/rights/copyrightpolicy.html)
  • the use of articles under ACM copyright is governed by the ACM copyright policy (available at http://www.acm.org/pubs/copyright_policy/)
  • technical reports and other articles issued by M‰lardalen University is free for personal use. For other use, the explicit consent of the authors is required
  • in other cases, please contact the copyright owner for detailed information

By accepting I agree to acknowledge and respect the rights of the copyright owner of the document I am about to access.

If you are in doubt, feel free to contact webmaster@ide.mdh.se

Fast and Robust Approximation of Smallest Enclosing Balls in Arbitrary Dimensions

Publication Type:

Journal article

Venue:

Computer Graphics Forum

Publisher:

Blackwell Publishing Ltd

DOI:

10.1111/cgf.12176


Abstract

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.

Bibtex

@article{Larsson3017,
author = {Thomas Larsson and Linus K{\"a}llberg},
title = {Fast and Robust Approximation of Smallest Enclosing Balls in Arbitrary Dimensions},
volume = {32},
number = {5},
pages = {93--101},
month = {August},
year = {2013},
journal = {Computer Graphics Forum},
publisher = {Blackwell Publishing Ltd},
url = {http://www.es.mdh.se/publications/3017-}
}