04441nam 2200625 450 991080922440332120180327123650.00-8218-8132-90-8218-4239-0(CKB)3240000000069979(EBL)3113314(SSID)ssj0000629463(PQKBManifestationID)11370059(PQKBTitleCode)TC0000629463(PQKBWorkID)10731738(PQKB)11787973(MiAaPQ)EBC3113314(RPAM)15118340(PPN)19710780X(EXLCZ)99324000000006997920071219h20082008 uy| 0engur|n|---|||||txtccrSurveys 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, editorsProvidence, Rhode Island :American Mathematical Society,[2008]©20081 online resource (568 p.)Contemporary mathematics,0271-4132 ;453Description based upon print version of record.Includes bibliographical references.""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""""The kissing number, blocking number and covering number of a convex body""""Open problems""Contemporary mathematics (American Mathematical Society) ;v. 453.Combinatorial geometryCongressesGeometryData processingCongressesCombinatorial geometryGeometryData processing516/.13Goodman Jacob E.Pach JánosPollack RichardAMS-IMS-SIAM Joint Summer Research Conference Discrete and Computational Geometry - Twenty Years Later(2006 :Snowbird, Utah),MiAaPQMiAaPQMiAaPQBOOK9910809224403321Surveys on discrete and computational geometry717977UNINA