Forbidden Configurations in Discrete Geometry PDF Download
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Author: David Eppstein
Publisher: Cambridge University Press
ISBN: 1108542972
Category : Computers
Languages : en
Pages : 242
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Book Description
This book surveys the mathematical and computational properties of finite sets of points in the plane, covering recent breakthroughs on important problems in discrete geometry, and listing many open problems. It unifies these mathematical and computational views using forbidden configurations, which are patterns that cannot appear in sets with a given property, and explores the implications of this unified view. Written with minimal prerequisites and featuring plenty of figures, this engaging book will be of interest to undergraduate students and researchers in mathematics and computer science. Most topics are introduced with a related puzzle or brain-teaser. The topics range from abstract issues of collinearity, convexity, and general position to more applied areas including robust statistical estimation and network visualization, with connections to related areas of mathematics including number theory, graph theory, and the theory of permutation patterns. Pseudocode is included for many algorithms that compute properties of point sets.
Author: David Eppstein
Publisher: Cambridge University Press
ISBN: 1108542972
Category : Computers
Languages : en
Pages : 242
Get Book Here
Book Description
This book surveys the mathematical and computational properties of finite sets of points in the plane, covering recent breakthroughs on important problems in discrete geometry, and listing many open problems. It unifies these mathematical and computational views using forbidden configurations, which are patterns that cannot appear in sets with a given property, and explores the implications of this unified view. Written with minimal prerequisites and featuring plenty of figures, this engaging book will be of interest to undergraduate students and researchers in mathematics and computer science. Most topics are introduced with a related puzzle or brain-teaser. The topics range from abstract issues of collinearity, convexity, and general position to more applied areas including robust statistical estimation and network visualization, with connections to related areas of mathematics including number theory, graph theory, and the theory of permutation patterns. Pseudocode is included for many algorithms that compute properties of point sets.
Author: David Eppstein
Publisher: Cambridge University Press
ISBN: 1108423914
Category : Computers
Languages : en
Pages : 241
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Book Description
Unifies discrete and computational geometry by using forbidden patterns of points to characterize many of its problems.
Author: David Eppstein
Publisher: Cambridge University Press
ISBN: 1108540279
Category : Computers
Languages : en
Pages : 241
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Book Description
This book surveys the mathematical and computational properties of finite sets of points in the plane, covering recent breakthroughs on important problems in discrete geometry, and listing many open problems. It unifies these mathematical and computational views using forbidden configurations, which are patterns that cannot appear in sets with a given property, and explores the implications of this unified view. Written with minimal prerequisites and featuring plenty of figures, this engaging book will be of interest to undergraduate students and researchers in mathematics and computer science. Most topics are introduced with a related puzzle or brain-teaser. The topics range from abstract issues of collinearity, convexity, and general position to more applied areas including robust statistical estimation and network visualization, with connections to related areas of mathematics including number theory, graph theory, and the theory of permutation patterns. Pseudocode is included for many algorithms that compute properties of point sets.
Author: Andras Bezdek
Publisher: CRC Press
ISBN: 0824747615
Category : Mathematics
Languages : en
Pages : 500
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Book Description
Celebrating the work of Professor W. Kuperberg, this reference explores packing and covering theory, tilings, combinatorial and computational geometry, and convexity, featuring an extensive collection of problems compiled at the Discrete Geometry Special Session of the American Mathematical Society in New Orleans, Louisiana. Discrete Geometry analyzes packings and coverings with congruent convex bodies , arrangements on the sphere, line transversals, Euclidean and spherical tilings, geometric graphs, polygons and polyhedra, and fixing systems for convex figures. This text also offers research and contributions from more than 50 esteemed international authorities, making it a valuable addition to any mathematical library.
Author: Peter Brass
Publisher: Springer Science & Business Media
ISBN: 0387299297
Category : Mathematics
Languages : en
Pages : 507
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Book Description
This book is the result of a 25-year-old project and comprises a collection of more than 500 attractive open problems in the field. The largely self-contained chapters provide a broad overview of discrete geometry, along with historical details and the most important partial results related to these problems. This book is intended as a source book for both professional mathematicians and graduate students who love beautiful mathematical questions, are willing to spend sleepless nights thinking about them, and who would like to get involved in mathematical research.
Author: Csaba D. Toth
Publisher: CRC Press
ISBN: 1351645919
Category : Computers
Languages : en
Pages : 2354
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Book Description
The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.
Author: Achille Braquelaire
Publisher: Springer Science & Business Media
ISBN: 3540433805
Category : Computers
Languages : en
Pages : 450
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Book Description
This book constitutes the refereed proceedings of the 10th International Conference on Digital Geometry for Computer Imagery, DGCI 2002, held in Bordeaux, France, in April 2002. The 22 revised full papers and 13 posters presented together with 3 invited papers were carefully reviewed and selected from 67 submissions. The papers are organized in topical sections on topology, combinatorial image analysis, morphological analysis, shape representation, models for discrete geometry, segmentation and shape recognition, and applications.
Author: Daniel Archambault
Publisher: Springer Nature
ISBN: 303035802X
Category : Computers
Languages : en
Pages : 624
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Book Description
This book constitutes the refereed proceedings of the 27th International Symposium on Graph Drawing and Network Visualization, GD 2019, held in Prague, Czech Republic, in September 2019. The 42 papers and 12 posters presented in this volume were carefully reviewed and selected from 113 submissions. They were organized into the following topical sections: Cartograms and Intersection Graphs, Geometric Graph Theory, Clustering, Quality Metrics, Arrangements, A Low Number of Crossings, Best Paper in Track 1, Morphing and Planarity, Parameterized Complexity, Collinearities, Topological Graph Theory, Best Paper in Track 2, Level Planarity, Graph Drawing Contest Report, and Poster Abstracts.
Author: Chi-Yeh Chen
Publisher: Springer Nature
ISBN: 3030895432
Category : Computers
Languages : en
Pages : 699
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Book Description
This book constitutes the proceedings of the 27th International Conference on Computing and Combinatorics, COCOON 2021, held in Tainan, Taiwan, in October 2021. Due to the COVID-19 pandemic, COCOON 2021 was organized as a hybrid conference. The 56 papers presented in this volume were carefully reviewed and selected from 131 submissions. The papers are divided into the following topical sub-headings: algorithms, approximation algorithms, automata, computational geometry, fault tolerant computing and fault diagnosis, graph algorithms, graph theory and applications, network and algorithms, online algorithm and stream algorithms, parameterized complexity and algorithms, and recreational games.
Author: Jiri Matousek
Publisher: Springer Science & Business Media
ISBN: 1461300398
Category : Mathematics
Languages : en
Pages : 491
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Book Description
The main topics in this introductory text to discrete geometry include basics on convex sets, convex polytopes and hyperplane arrangements, combinatorial complexity of geometric configurations, intersection patterns and transversals of convex sets, geometric Ramsey-type results, and embeddings of finite metric spaces into normed spaces. In each area, the text explains several key results and methods.
