The Kissing Number Problem: A New Result from Global Optimization

Leo Liberti; Nelson Maculan; Sergei Kucherenko

doi:10.1016/j.endm.2004.03.040

The Kissing Number Problem: A New Result from Global Optimization

Leo Liberti
, Nelson Maculan
, Sergei Kucherenko

Politecnico di Milano
Instituto de Biofisica da UFRJ
Imperial College London

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

3 Citations (Scopus)

Résumé

Determining the maximum number of D-dimensional spheres of radius r that can be adjacent to a central sphere of radius r is known as the Kissing Number Problem (KNP). The problem has been solved for 2 and 3 dimensions. The smallest open case is 4 dimensions: a solution with 24 spheres is known, and an upper bound of 25 has been found. We present a new nonlinear mathematical programming model for the solution of the KNP. This problem is solved using a quasi Monte Carlo variant of a multi level single linkage algorithm for global optimization. The numerical results indicate that the solution of the KNP is 24 spheres, and not 25.

langue originale	Anglais
Pages (de - à)	203-207
Nombre de pages	5
journal	Electronic Notes in Discrete Mathematics
Volume	17
Les DOIs	https://doi.org/10.1016/j.endm.2004.03.040
état	Publié - 20 oct. 2004
Modification externe	Oui

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10.1016/j.endm.2004.03.040

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title = "The Kissing Number Problem: A New Result from Global Optimization",

abstract = "Determining the maximum number of D-dimensional spheres of radius r that can be adjacent to a central sphere of radius r is known as the Kissing Number Problem (KNP). The problem has been solved for 2 and 3 dimensions. The smallest open case is 4 dimensions: a solution with 24 spheres is known, and an upper bound of 25 has been found. We present a new nonlinear mathematical programming model for the solution of the KNP. This problem is solved using a quasi Monte Carlo variant of a multi level single linkage algorithm for global optimization. The numerical results indicate that the solution of the KNP is 24 spheres, and not 25.",

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T2 - A New Result from Global Optimization

AU - Liberti, Leo

AU - Maculan, Nelson

AU - Kucherenko, Sergei

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Y1 - 2004/10/20

N2 - Determining the maximum number of D-dimensional spheres of radius r that can be adjacent to a central sphere of radius r is known as the Kissing Number Problem (KNP). The problem has been solved for 2 and 3 dimensions. The smallest open case is 4 dimensions: a solution with 24 spheres is known, and an upper bound of 25 has been found. We present a new nonlinear mathematical programming model for the solution of the KNP. This problem is solved using a quasi Monte Carlo variant of a multi level single linkage algorithm for global optimization. The numerical results indicate that the solution of the KNP is 24 spheres, and not 25.

AB - Determining the maximum number of D-dimensional spheres of radius r that can be adjacent to a central sphere of radius r is known as the Kissing Number Problem (KNP). The problem has been solved for 2 and 3 dimensions. The smallest open case is 4 dimensions: a solution with 24 spheres is known, and an upper bound of 25 has been found. We present a new nonlinear mathematical programming model for the solution of the KNP. This problem is solved using a quasi Monte Carlo variant of a multi level single linkage algorithm for global optimization. The numerical results indicate that the solution of the KNP is 24 spheres, and not 25.

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DO - 10.1016/j.endm.2004.03.040

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JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

ER -

The Kissing Number Problem: A New Result from Global Optimization

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