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Record Nr. |
UNINA9910809224403321 |
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Titolo |
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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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , [2008] |
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©2008 |
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ISBN |
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0-8218-8132-9 |
0-8218-4239-0 |
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Descrizione fisica |
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1 online resource (568 p.) |
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Collana |
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Contemporary mathematics, , 0271-4132 ; ; 453 |
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Disciplina |
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Soggetti |
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Combinatorial geometry |
Geometry - Data processing |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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""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"" |
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""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"" |
""The kissing number, blocking number and covering number of a convex body""""Open problems"" |
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