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Fast and robust approximation of smallest enclosing balls in arbitrary dimensions
Mälardalen University, School of Innovation, Design and Engineering.ORCID iD: 0000-0002-1550-0994
Mälardalen University, School of Innovation, Design and Engineering.ORCID iD: 0000-0002-6969-6793
2013 (English)In: Computer graphics forum (Print), ISSN 0167-7055, E-ISSN 1467-8659, Vol. 32, no 5, p. 93-101Article in journal (Refereed) Published
Abstract [en]

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. 

Place, publisher, year, edition, pages
2013. Vol. 32, no 5, p. 93-101
Keywords [en]
Arbitrary dimension, Empirical evaluations, General class, High dimensions, Large problems, Reliable results, Robust approximations, Theoretical arguments, Computer graphics, Approximation algorithms
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:mdh:diva-21268DOI: 10.1111/cgf.12176ISI: 000323204000010Scopus ID: 2-s2.0-84882797817OAI: oai:DiVA.org:mdh-21268DiVA, id: diva2:646057
Available from: 2013-09-06 Created: 2013-09-06 Last updated: 2018-02-23Bibliographically approved

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Larsson, Thomas BKällberg, Linus

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