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

• Main Authors: Szabó, P. G. (Author), Markót, M. Cs (Author), Csendes, T. (Author), Specht, E. (Author), Casado, L. G. (Author), García, I. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Springer US, 2007.
• Series: Springer Optimization and Its Applications, 6
• Subjects: Mathematics.; Arithmetic and logic units, Computer.; Computer science > Mathematics.; Computer mathematics.; Convex geometry.; Discrete geometry.; Mathematical optimization.; Optimization.; Math Applications in Computer Science.; Convex and Discrete Geometry.; Arithmetic and Logic Structures.; Computational Science and Engineering.

In one sense, the problem of finding the densest packing of congruent circles in a square is easy to understand: it is a matter of positioning a given number of equal circles in such a way that the circles fit fully in a square without overlapping. But on closer inspection, this problem reveals itse...

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.