Algorithms in Combinatorial Geometry

Algorithms in Combinatorial Geometry
Author: Herbert Edelsbrunner
Publisher: Springer Science & Business Media
Total Pages: 423
Release: 2012-12-06
Genre: Computers
ISBN: 3642615686

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Computational geometry as an area of research in its own right emerged in the early seventies of this century. Right from the beginning, it was obvious that strong connections of various kinds exist to questions studied in the considerably older field of combinatorial geometry. For example, the combinatorial structure of a geometric problem usually decides which algorithmic method solves the problem most efficiently. Furthermore, the analysis of an algorithm often requires a great deal of combinatorial knowledge. As it turns out, however, the connection between the two research areas commonly referred to as computa tional geometry and combinatorial geometry is not as lop-sided as it appears. Indeed, the interest in computational issues in geometry gives a new and con structive direction to the combinatorial study of geometry. It is the intention of this book to demonstrate that computational and com binatorial investigations in geometry are doomed to profit from each other. To reach this goal, I designed this book to consist of three parts, acorn binatorial part, a computational part, and one that presents applications of the results of the first two parts. The choice of the topics covered in this book was guided by my attempt to describe the most fundamental algorithms in computational geometry that have an interesting combinatorial structure. In this early stage geometric transforms played an important role as they reveal connections between seemingly unrelated problems and thus help to structure the field.


Algorithms in Combinatorial Geometry
Language: en
Pages: 446
Authors: Herbert Edelsbrunner
Categories: Computers
Type: BOOK - Published: 1987-07-31 - Publisher: Springer Science & Business Media

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Computational geometry as an area of research in its own right emerged in the early seventies of this century. Right from the beginning, it was obvious that str
Geometric Algorithms and Combinatorial Optimization
Language: en
Pages: 374
Authors: Martin Grötschel
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

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Historically, there is a close connection between geometry and optImization. This is illustrated by methods like the gradient method and the simplex method, whi
Combinatorial Geometry
Language: en
Pages: 376
Authors: János Pach
Categories: Mathematics
Type: BOOK - Published: 2011-10-18 - Publisher: John Wiley & Sons

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A complete, self-contained introduction to a powerful and resurgingmathematical discipline . Combinatorial Geometry presents andexplains with complete proofs so
Algorithms in Combinatorial Geometry
Language: en
Pages: 423
Authors: Herbert Edelsbrunner
Categories: Computers
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

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Computational geometry as an area of research in its own right emerged in the early seventies of this century. Right from the beginning, it was obvious that str
Combinatorial Algorithms
Language: en
Pages: 346
Authors: Donald L. Kreher
Categories: Mathematics
Type: BOOK - Published: 1998-12-18 - Publisher: CRC Press

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This textbook thoroughly outlines combinatorial algorithms for generation, enumeration, and search. Topics include backtracking and heuristic search methods app