Overview
- Summarizes the results of recent years in circle packing into the unit square, emphasizing the algorithmic and optimization details
- Reports the source codes that have provided the new results
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Optimization and Its Applications (SOIA, volume 6)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents(12 chapters)
About this book
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.
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)
Authors and Affiliations
-
University of Szeged, Hungary
P. G. Szabó, T. Csendes
-
Hungarian Academy of Sciences, Budapest, Hungary
M. Cs. Markót
-
Otto von Guericke University of Magdeburg, Germany
E. Specht
-
University of Almería, Spain
L. G. Casado, I. García
Bibliographic Information
Book Title: New Approaches to Circle Packing in a Square
Book Subtitle: With Program Codes
Authors: P. G. Szabó, M. Cs. Markót, T. Csendes, E. Specht, L. G. Casado, I. García
Series Title: Springer Optimization and Its Applications
DOI: https://doi.org/10.1007/978-0-387-45676-8
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag US 2007
Hardcover ISBN: 978-0-387-45673-7Published: 02 March 2007
Softcover ISBN: 978-1-4899-8897-3Published: 19 November 2014
eBook ISBN: 978-0-387-45676-8Published: 31 May 2007
Series ISSN: 1931-6828
Series E-ISSN: 1931-6836
Edition Number: 1
Number of Pages: XIV, 238
Topics: Optimization, Math Applications in Computer Science, Convex and Discrete Geometry, Arithmetic and Logic Structures, Computational Science and Engineering