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Combinatorial Geometry and Its Algorithmic Applications: The Alcalá Lectures
 
János Pach Courant Institute of Mathematical Sciences, New York, NY
Micha Sharir Tel Aviv University, Tel Aviv, Israel
Front Cover for Combinatorial Geometry and Its Algorithmic Applications
Available Formats:
Hardcover ISBN: 978-0-8218-4691-9
Product Code: SURV/152
235 pp 
List Price: $86.00
MAA Member Price: $77.40
AMS Member Price: $68.80
Electronic ISBN: 978-1-4704-1379-8
Product Code: SURV/152.E
235 pp 
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $64.80
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
Front Cover for Combinatorial Geometry and Its Algorithmic Applications
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  • Front Cover for Combinatorial Geometry and Its Algorithmic Applications
  • Back Cover for Combinatorial Geometry and Its Algorithmic Applications
Combinatorial Geometry and Its Algorithmic Applications: The Alcalá Lectures
János Pach Courant Institute of Mathematical Sciences, New York, NY
Micha Sharir Tel Aviv University, Tel Aviv, Israel
Available Formats:
Hardcover ISBN:  978-0-8218-4691-9
Product Code:  SURV/152
235 pp 
List Price: $86.00
MAA Member Price: $77.40
AMS Member Price: $68.80
Electronic ISBN:  978-1-4704-1379-8
Product Code:  SURV/152.E
235 pp 
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $64.80
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 1522009
    MSC: Primary 05; 52; 68;

    Based on a lecture series given by the authors at a satellite meeting of the 2006 International Congress of Mathematicians and on many articles written by them and their collaborators, this volume provides a comprehensive up-to-date survey of several core areas of combinatorial geometry. It describes the beginnings of the subject, going back to the nineteenth century (if not to Euclid), and explains why counting incidences and estimating the combinatorial complexity of various arrangements of geometric objects became the theoretical backbone of computational geometry in the 1980s and 1990s. The combinatorial techniques outlined in this book have found applications in many areas of computer science from graph drawing through hidden surface removal and motion planning to frequency allocation in cellular networks.

    Combinatorial Geometry and Its Algorithmic Applications is intended as a source book for professional mathematicians and computer scientists as well as for graduate students interested in combinatorics and geometry. Most chapters start with an attractive, simply formulated, but often difficult and only partially answered mathematical question, and describes the most efficient techniques developed for its solution. The text includes many challenging open problems, figures, and an extensive bibliography.

    Readership

    Graduate students and research mathematicians interested in combinatorial geometry and algorithmic applications.

  • Table of Contents
     
     
    • Chapters
    • 1. Sylvester-Gallai problem: The beginnings of combinatorial geometry
    • 2. Arrangements of surfaces: Evolution of the basic theory
    • 3. Davenport-Schinzel sequences: The inverse Ackermann function in geometry
    • 4. Incidences and their relatives: From Szemerédi and Trotter to cutting lenses
    • 5. Crossing numbers of graphs: Graph drawing and its applications
    • 6. Extremal combinatorics: Repeated patterns and pattern recognition
    • 7. Lines in space: From ray shooting to geometric transversals
    • 8. Geometric coloring problems: Sphere packings and frequency allocation
    • 9. From Sam Loyd and László Fejes Tóth: The 15 puzzle and motion planning
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Volume: 1522009
MSC: Primary 05; 52; 68;

Based on a lecture series given by the authors at a satellite meeting of the 2006 International Congress of Mathematicians and on many articles written by them and their collaborators, this volume provides a comprehensive up-to-date survey of several core areas of combinatorial geometry. It describes the beginnings of the subject, going back to the nineteenth century (if not to Euclid), and explains why counting incidences and estimating the combinatorial complexity of various arrangements of geometric objects became the theoretical backbone of computational geometry in the 1980s and 1990s. The combinatorial techniques outlined in this book have found applications in many areas of computer science from graph drawing through hidden surface removal and motion planning to frequency allocation in cellular networks.

Combinatorial Geometry and Its Algorithmic Applications is intended as a source book for professional mathematicians and computer scientists as well as for graduate students interested in combinatorics and geometry. Most chapters start with an attractive, simply formulated, but often difficult and only partially answered mathematical question, and describes the most efficient techniques developed for its solution. The text includes many challenging open problems, figures, and an extensive bibliography.

Readership

Graduate students and research mathematicians interested in combinatorial geometry and algorithmic applications.

  • Chapters
  • 1. Sylvester-Gallai problem: The beginnings of combinatorial geometry
  • 2. Arrangements of surfaces: Evolution of the basic theory
  • 3. Davenport-Schinzel sequences: The inverse Ackermann function in geometry
  • 4. Incidences and their relatives: From Szemerédi and Trotter to cutting lenses
  • 5. Crossing numbers of graphs: Graph drawing and its applications
  • 6. Extremal combinatorics: Repeated patterns and pattern recognition
  • 7. Lines in space: From ray shooting to geometric transversals
  • 8. Geometric coloring problems: Sphere packings and frequency allocation
  • 9. From Sam Loyd and László Fejes Tóth: The 15 puzzle and motion planning
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