New Approaches to Circle Packing in a Square

With Program Codes

Péter Gábor Szabó, Mihaly Csaba Markót, Tibor Csendes, Eckard Specht, Leocadio G. Casado (Autoren)

Buch | Softcover

238 Seiten

2014 | 2007 ed.
Springer-Verlag New York Inc.
978-1-4899-8897-3 (ISBN)

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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.

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.

Erscheint lt. Verlag	19.11.2014
Reihe/Serie	Springer Optimization and Its Applications ; 6
Zusatzinfo	XIV, 238 p.
Verlagsort	New York
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Informatik ► Theorie / Studium ► Algorithmen
	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	1-4899-8897-1 / 1489988971
ISBN-13	978-1-4899-8897-3 / 9781489988973
Zustand	Neuware