Communications in Information and Systems

Volume 12 (2012)

Number 3

Smallest enclosing ball multidistance

Pages: 185 – 194

DOI: http://dx.doi.org/10.4310/CIS.2012.v12.n3.a1

Authors

I. Aguiló (Department of Mathematics and Computer Science, University of the Balearic Islands, Palma de Mallorca, Spain)

J. Martín (Department of Mathematics and Computer Science, University of the Balearic Islands, Palma de Mallorca, Spain)

G. Mayor (Department of Mathematics and Computer Science, University of the Balearic Islands, Palma de Mallorca, Spain)

J. Suñer (Department of Mathematics and Computer Science, University of the Balearic Islands, Palma de Mallorca, Spain)

O. Valero (Department of Mathematics and Computer Science, University of the Balearic Islands, Palma de Mallorca, Spain)

Abstract

The smallest enclosing ball problem is analyzed in the class of proper metric spaces. By using the diameter of the smallest enclosing ball of a set of points, we find conditions in order to ensure that the mentioned measure is a multidistance.

Keywords

metric space, Fermat multidistance, smallest enclosing ball, midpoint property, Fermat property, $m$-dimensional Euclidian space

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