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Vietnam Journal of Mathematics 40:2&3(2012)
345-354
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A Model to the Ellipsoidal Filling Problem
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Roberto Quirino do Nascimento1,
Ana Flavia U. S. Macambira1,
Lucidio dos Anjos Formiga Cabral1 and
Nelson Maculan2
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1Universidade
Federal da Paraiba, Departamento de Informatica,
58.051-900 - Joao Pessoa, Paraiba, Brazil
2 Universidade
Federal do Rio de Janeiro,
COPPE-Engenharia de Sistemas e Computação,
Caixa
Postal 68511, 21941-972 Rio de Janeiro, RJ, Brasil
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Dedicated to Professor
Phan Quoc Khanh on the occasion of his 65th birthday
Received November 6,
2011
Revised April 16, 2012
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Abstract. The ellipsoidal filling problem consists
in covering an ellipsoid with spheres whose radii belong to a discrete set.
The discrete nature of the radii of the spheres is one of the difficulties
inherent to this problem when one tries to solve it and another dificulty
is ensuring that every point of the ellipsoid is covered by at least one
sphere. Despite these difficulties, a good reason to study this problem is
its application in configuring Gamma ray machines, used in brain tumors
treatments. This problem is a semi-infinite nonlinear discrete one and we
present a weak version that uses the idea of the Facility Location Problem
to determine a likely location for the center of the spheres in such a way
that the ellipsoid must be filled by them.
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2000 Mathematics
Subject Classification. 90C11.
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Keywords.
Discrete optimization, global optimization, Gamma Knife.
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Vietnam
Academy of Science and Technology &
Vietnamese Mathematical Society
©
Copyright Vietnam Journal of
Mathematics. All rights reserved.
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