LEADER 04441nam 2200625 450 001 9910809224403321 005 20180327123650.0 010 $a0-8218-8132-9 010 $a0-8218-4239-0 035 $a(CKB)3240000000069979 035 $a(EBL)3113314 035 $a(SSID)ssj0000629463 035 $a(PQKBManifestationID)11370059 035 $a(PQKBTitleCode)TC0000629463 035 $a(PQKBWorkID)10731738 035 $a(PQKB)11787973 035 $a(MiAaPQ)EBC3113314 035 $a(RPAM)15118340 035 $a(PPN)19710780X 035 $a(EXLCZ)993240000000069979 100 $a20071219h20082008 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aSurveys on discrete and computational geometry $etwenty years later : AMS-IMS-SIAM Joint Summer Research Conference, June 18-22, 2006, Snowbird, Utah /$fJacob E. Goodman, Ja?nos Pach, Richard Pollack, editors 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2008] 210 4$dİ2008 215 $a1 online resource (568 p.) 225 1 $aContemporary mathematics,$x0271-4132 ;$v453 300 $aDescription based upon print version of record. 320 $aIncludes bibliographical references. 327 $a""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 a??? recent progress and open problems""; ""1. Introduction""; ""2. Semi-algebraic Geometry: Background"" 327 $a""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 a??? right?""; ""Persistent homologya???a survey""; ""Recent progress on line transversals to families of translated ovals""; ""An improved, simple construction of many halving edges""; ""Unfolding orthogonal polyhedra"" 327 $a""The discharging method in combinatorial geometry and the Pach-Sharir conjecture""""Pseudo-triangulationsa???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"" 327 $a""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 ErdA??s-Szekeres type problem for interior points"" 327 $a""The kissing number, blocking number and covering number of a convex body""""Open problems"" 410 0$aContemporary mathematics (American Mathematical Society) ;$vv. 453. 606 $aCombinatorial geometry$vCongresses 606 $aGeometry$xData processing$vCongresses 615 0$aCombinatorial geometry 615 0$aGeometry$xData processing 676 $a516/.13 702 $aGoodman$b Jacob E. 702 $aPach$b Ja?nos 702 $aPollack$b Richard 712 12$aAMS-IMS-SIAM Joint Summer Research Conference Discrete and Computational Geometry - Twenty Years Later$f(2006 :$eSnowbird, Utah), 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910809224403321 996 $aSurveys on discrete and computational geometry$9717977 997 $aUNINA