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Discrete and Computational Geometry

The Goodman-Pollack Festschrift

  • Book
  • © 2003

Overview

Editors:
  1. Boris Aronov

    1. Department of Computer and Information Science, Polytechnic University, Six Metro Tech Center, Brooklyn, USA

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  2. Saugata Basu

    1. School of Mathematics, Georgia Institute of Technology, Atlanta, USA

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  3. János Pach

    1. City College and Courant Institute, New York, USA

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  4. Micha Sharir

    1. School of Computer Science, Tel Aviv University, Tel Aviv, Israel

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  • Unique volume summarising the state of the art in its field
  • Collection of the world's top authors

Part of the book series: Algorithms and Combinatorics (AC, volume 25)

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Table of contents (41 chapters)

  1. Front Matter

    Pages I-XII
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  2. On the Complexity of Many Faces in Arrangements of Pseudo-Segments and Circles

    • Pankaj K. Agarwal, Boris Aronov, Micha Sharir
    Pages 1-24

  3. Polyhedral Cones of Magic Cubes and Squares

    • Maya Ahmed, Jesús De Loera, Raymond Hemmecke
    Pages 25-41

  4. Congruent Dudeney Dissections of Triangles and Convex Quadrilaterals – All Hinge Points Interior to the Sides of the Polygons

    • Jin Akiyama, Gisaku Nakamura
    Pages 43-63

  5. Computing the Hausdorff Distance of Geometric Patterns and Shapes

    • Helmut Alt, Peter Braß, Michael Godau, Christian Knauer, Carola Wenk
    Pages 65-76

  6. A Sum of Squares Theorem for Visibility Complexes and Applications

    • Pierre Angelier, Michel Pocchiola
    Pages 77-137

  7. On the Reflexivity of Point Sets

    • Esther M. Arkin, Joseph S. B. Mitchell, Sándor P. Fekete, Ferran Hurtado, Marc Noy, Vera Sacristán et al.
    Pages 139-156

  8. Geometric Permutations of Large Families of Translates

    • Andrei Asinowski, Meir Katchalski, Andreas Holmsen, Helge Tverberg
    Pages 157-176

  9. Integer Points in Rotating Convex Bodies

    • Imre Bárány, Jiří Matoušek
    Pages 177-201

  10. Complex Matroids Phirotopes and Their Realizations in Rank 2

    • Alexander Below, Vanessa Krummeck, Jürgen Richter-Gebert
    Pages 203-233

  11. Covering the Sphere by Equal Spherical Balls

    • Károly Böröczky Jr., Gergely Wintsche
    Pages 235-251

  12. Lower Bounds for High Dimensional Nearest Neighbor Search and Related Problems

    • Allan Borodin, Rafail Ostrovsky, Yuval Rabani
    Pages 253-274

  13. A Turán-type Extremal Theory of Convex Geometric Graphs

    • Peter Brass, Gyula Károlyi, Pavel Valtr
    Pages 275-300

  14. On the Inapproximability of Polynomial-programming, the Geometry of Stable Sets, and the Power of Relaxation

    • Andreas Brieden, Peter Gritzmann
    Pages 301-311

  15. A Lower Bound on the Complexity of Approximate Nearest-Neighbor Searching on the Hamming Cube

    • Amit Chakrabarti, Bernard Chazelle, Benjamin Gum, Alexey Lvov
    Pages 313-328

  16. Detecting Undersampling in Surface Reconstruction

    • Tamal K. Dey, Joachim Giesen
    Pages 329-345

  17. A Survey of the Hadwiger-Debrunner (p, q)-problem

    • Jürgen Eckhoff
    Pages 347-377

  18. Surface Reconstruction by Wrapping Finite Sets in Space

    • Herbert Edelsbrunner
    Pages 379-404

  19. Infeasibility of Systems of Halfspaces

    • Stefan Felsner, Nicole Morawe
    Pages 405-424

  20. Combinatorial Generation of Small Point Configurations and Hyperplane Arrangements

    • Lukas Finschi, Komei Fukuda
    Pages 425-440
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Keywords

About this book

This is an impressive collection of original research papers in discrete and computational geometry, contributed by many leading researchers in these fields, as a tribute to Jacob E. Goodman and Richard Pollack, two of the `founding fathers' of the area, on the occasion of their 2/3 x 100 birthdays. The topics covered by the 41 papers provide professionals and graduate students with a comprehensive presentation of the state of the art in most aspects of discrete and computational geometry, including geometric algorithms, arrangements, geometric graph theory and quantitative and algorithmic real algebraic geometry, with important connections to algebraic geometry, convexity, polyhedral combinatorics, and the theory of packing, covering, and tiling.

The book will serve as an invaluable source of reference in this discipline, and an indispensible component of the library of anyone working in the above areas.

Editors and Affiliations

  • Department of Computer and Information Science, Polytechnic University, Six Metro Tech Center, Brooklyn, USA

    Boris Aronov

  • School of Mathematics, Georgia Institute of Technology, Atlanta, USA

    Saugata Basu

  • City College and Courant Institute, New York, USA

    János Pach

  • School of Computer Science, Tel Aviv University, Tel Aviv, Israel

    Micha Sharir

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