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Identification and elimination of interior points for the minimum enclosing ball problem

Identification and elimination of interior points for the minimum enclosing ball problem
Identification and elimination of interior points for the minimum enclosing ball problem
Given ${\cal A} := \{a^1,\dots,a^m\} \subset \mathbb{R}^n$, we consider the problem of reducing the input set for the computation of the minimum enclosing ball of ${\cal A}$. In this note, given an approximate solution to the minimum enclosing ball problem, we propose a simple procedure to identify and eliminate points in ${\cal A}$ that are guaranteed to lie in the interior of the minimum-radius ball enclosing ${\cal A}$. Our computational results reveal that incorporating this procedure into two recent algorithms proposed by Yıldırım lead to significant speed-ups in running times especially for randomly generated large-scale problems. We also illustrate that the extra overhead due to the elimination procedure remains at an acceptable level for spherical or almost spherical input sets.


minimum enclosing balls, input set reduction, approximation algorithms
1052-6234
1392-1396
Ahipasaoglu, Selin D.
d69f1b80-5c05-4d50-82df-c13b87b02687
Yildirim, E. Alper
fc7f886b-1d12-43b8-89aa-70c6424384db
Ahipasaoglu, Selin D.
d69f1b80-5c05-4d50-82df-c13b87b02687
Yildirim, E. Alper
fc7f886b-1d12-43b8-89aa-70c6424384db

Ahipasaoglu, Selin D. and Yildirim, E. Alper (2008) Identification and elimination of interior points for the minimum enclosing ball problem. SIAM Journal on Optimization, 19 (3), 1392-1396. (doi:10.1137/080727208).

Record type: Article

Abstract

Given ${\cal A} := \{a^1,\dots,a^m\} \subset \mathbb{R}^n$, we consider the problem of reducing the input set for the computation of the minimum enclosing ball of ${\cal A}$. In this note, given an approximate solution to the minimum enclosing ball problem, we propose a simple procedure to identify and eliminate points in ${\cal A}$ that are guaranteed to lie in the interior of the minimum-radius ball enclosing ${\cal A}$. Our computational results reveal that incorporating this procedure into two recent algorithms proposed by Yıldırım lead to significant speed-ups in running times especially for randomly generated large-scale problems. We also illustrate that the extra overhead due to the elimination procedure remains at an acceptable level for spherical or almost spherical input sets.


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More information

Published date: 1 November 2008
Keywords: minimum enclosing balls, input set reduction, approximation algorithms

Identifiers

Local EPrints ID: 443142
URI: http://eprints.soton.ac.uk/id/eprint/443142
ISSN: 1052-6234
PURE UUID: c6f7df0b-8923-44ec-b024-bdd5db26e63e
ORCID for Selin D. Ahipasaoglu: ORCID iD orcid.org/0000-0003-1371-315X

Catalogue record

Date deposited: 12 Aug 2020 16:31
Last modified: 24 Sep 2020 01:54

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Contributors

Author: E. Alper Yildirim

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