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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	203-207
Number of pages	5
Journal	Electronic Notes in Discrete Mathematics
Volume	17
DOIs	https://doi.org/10.1016/j.endm.2004.03.040
Publication status	Published - 20 Oct 2004
Externally published	Yes

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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.",

author = "Leo Liberti and Nelson Maculan and Sergei Kucherenko",

year = "2004",

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T1 - The Kissing Number Problem

T2 - A New Result from Global Optimization

AU - Liberti, Leo

AU - Maculan, Nelson

AU - Kucherenko, Sergei

PY - 2004/10/20

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.

U2 - 10.1016/j.endm.2004.03.040

DO - 10.1016/j.endm.2004.03.040

M3 - Article

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SN - 1571-0653

VL - 17

SP - 203

EP - 207

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

ER -

The Kissing Number Problem: A New Result from Global Optimization

Abstract

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