New Approaches to Circle Packing in a Square: With Program Codes

by Péter Gábor Szabó, Mihaly Csaba Markót, Tibor Csendes, Eckard Specht, Leocadio G. Casado

Overview

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.

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.

Product Details

ISBN-13:	9780387456737
Publisher:	Springer US
Publication date:	03/02/2007
Series:	Springer Optimization and Its Applications , #6
Edition description:	2007
Pages:	238
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

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.

Editorial Reviews

From the reviews:

"The book under review gives a detailed survey on the achievements of the last years on the problem of finding densest packings … . The text is written in a very comprehensive and informative way, and all the numerical results on densities are impressively illustrated by many figures of ‘optimal’ packings. … will serve as an excellent source for everybody, expert on non-expert, who is interested in circle packing or, who is just interested in the hardness of an appealing problem in discrete geometry." (Martin Henk, Zentralblatt MATH, Vol. 1128 (6), 2008)

From the Publisher