Surveys on discrete and computational geometry : twenty years later : AMS-IMS-SIAM Joint Summer Research Conference, June 18-22, 2006, Snowbird, Utah

Surveys on discrete and computational geometry : twenty years later : AMS-IMS-SIAM Joint Summer Research Conference, June 18-22, 2006, Snowbird, Utah / Jacob E. Goodman, János Pach, Richard Pollack, editors.

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Bibliographic Details
Corporate Author: AMS-IMS-SIAM Joint Summer Research Conference Discrete and Computational Geometry - Twenty Years Later
Other Authors: Goodman, Jacob E. (Editor), Pach, János (Editor), Pollack, Richard (Editor)
Format: eBook
Language:English
Published: Providence, Rhode Island : American Mathematical Society, [2008]
Series:Contemporary mathematics (American Mathematical Society) ; v. 453.
Subjects:
Combinatorial geometry > Congresses.
Geometry > Data processing > Congresses.
Combinatorial geometry
Geometry > Data processing
Conference papers and proceedings
Online Access:Click for online access
Table of Contents:
  • ""Contents""; ""Preface""; ""Musings on discrete geometry and ""20 years of Discrete & Computational Geometry""""; ""State of the union (of geometric objects)""; ""Metric graph theory and geometry: a survey""; ""Extremal problems for convex lattice polytopes: a survey""; ""On simple arrangements of lines and pseudo-lines in P2 and R2 with the maximum number of triangles""; ""The computational complexity of convex bodies""; ""Algorithmic semi-algebraic geometry and topology â€? recent progress and open problems""; ""1. Introduction""; ""2. Semi-algebraic Geometry: Background""
  • ""3. Recent Algorithmic Results""""4. Algorithmic Preliminaries""; ""5. Topological Preliminaries""; ""6. Algorithms for Computing the First Few Betti Numbers""; ""7. The Quadratic Case""; ""8. Betti Numbers of Arrangements""; ""9. Open Problems""; ""Acknowledgment""; ""References""; ""Expansive motions""; ""All polygons flip finitely â€? right?""; ""Persistent homologyâ€?a survey""; ""Recent progress on line transversals to families of translated ovals""; ""An improved, simple construction of many halving edges""; ""Unfolding orthogonal polyhedra""
  • ""The discharging method in combinatorial geometry and the Pach-Sharir conjecture""""Pseudo-triangulationsâ€?a survey""; ""1. Introduction""; ""2. Basic Properties of Pseudo-Triangulations""; ""3. The Set of all Pseudo-Triangulations""; ""4. 3D Liftings and Locally Convex Functions""; ""5. Self-Stresses, Reciprocal Diagrams, and the Maxwell-Cremona Correspondence""; ""6. Pseudo-Triangulations and Rigidity""; ""7. Planar Rigid Graphs are Pseudo-Triangulations""; ""8. Polytopes of Pseudo-Triangulations""; ""9. Applications of Pseudo-Triangulations""; ""References""
  • ""Line problems in nonlinear computational geometry""""On empty hexagons""; ""k-sets and k-facets""; ""1. Introduction""; ""2. Preliminaries""; ""3. Random Sampling""; ""4. Special Point Sets""; ""5. Lower Bounds""; ""6. Upper Bounds for Halving Facets in All Dimensions""; ""7. Crossings in Dimension 2.""; ""8. Improvements in Three And Four Dimensions""; ""9. Convex Quadrilaterals""; ""10. Connections to the Combinatorial Theory of Convex Polytopes""; ""References""; ""An ErdÅ?s-Szekeres type problem for interior points""

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