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Surveys on discrete and comput...
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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
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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 � 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 � right?""; ""Persistent homology�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-triangulations�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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