New Approaches to Circle Packing in a Square by Szabó, Péter Gábor; Markót, Mihaly Csaba; Csendes, Tibor;

With Program Codes

Sorozatcím: Springer Optimization and Its Applications; 6;

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A termék adatai:

Kiadás sorszáma 2007
Kiadó Springer US
Megjelenés dátuma 2014. november 19.
Kötetek száma 1 pieces, Previously published in hardcover

ISBN 9781489988973
Kötéstípus Puhakötés
Lásd még 9780387456737
Terjedelem238 oldal
Méret 235x155 mm
Súly 454 g
Nyelv angol
Illusztrációk XIV, 238 p. Tables, black & white

Kategóriák

Hosszú leírás:

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.

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. Typical 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.

Több

Tartalomjegyzék:

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.

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