New Approaches to Circle Packing in a Square

With Program Codes

P. G. Szabo, M.C. Markot, T. Csendes, E. Specht, L. G. Casado, I. García - Collection Optimization and its Applications

252 pages, parution le 22/02/2007

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Résumé

In one sense, the problem of finding the densest packing of congruent circles in a square is easy to understand. But on closer inspection, this problem reveals itself to be an interesting challenge of discrete and computational geometry with all its surprising structural forms and regularities. This book summarizes results achieved in solving the circle packing problem over the past few years, providing the reader with a comprehensive view of both theoretical and computational achievements. Typically illustrations of problem solutions are shown, elegantly displaying the results obtained.

Beyond the theoretically challenging character of the problem, the solution methods developed in the book also have many practical applications.

One especially important feature of the book is the inclusion on an enclosed CD of all the open source programming codes used. Since the codes can be worked with directly, they will enable the reader to improve on them and solve problem instances that still remain challenging, or to use them as a starting point for solving related application problems.

Written for: Mathematicians, engineers, and students who are involved either in the design of constrained optimization algorithms, or in packing, covering problems, geometric optimization, or location theory

Sommaire

Introduction and Problem History
Problem Definitions and Formulations
Bounds for the Optimum Values
Approximate Circle Packings Using Optimization Methods
Other Methods for Finding Approximate Circle Packings
Interval Methods for Validating Optimal Solutions
The First Fully Interval-based Optimization Method
The Improved Version of the Interval Optimization Method
Interval Methods for Verifying Structural Optimality
Repeated Patterns in Circle Packings
Minimal Polynomials of Point Arrangements
About the Codes Used

A. Currently Best Known Results for Packing Congruent Circles in a Square

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	P. G. Szabo, M.C. Markot, T. Csendes, E. Specht, L. G. Casado, I. García
Collection	Optimization and its Applications
Parution	22/02/2007
Nb. de pages	252
Format	16 x 24
Couverture	Relié
Poids	570g
Intérieur	Noir et Blanc
EAN13	9780387456737
ISBN13	978-0-387-45673-7