Twentieth Anniversary Volume: Discrete & Computational Geometry

There Are Not Too Many Magic Configurations.- Computing the Detour and Spanning Ratio of Paths, Trees, and Cycles.- Robust Shape Fitting via Peeling and Grating Coresets.- Siegel's Lemma and Sum-Distinct Sets.- Slicing Convex Sets and Measures by a Hyperplane.- A Centrally Symmetric Version of the Cyclic Polytope.- On Projections of Semi-Algebraic Sets Defined by Few Quadratic Inequalities.- Enumeration in Convex Geometries and Associated Polytopal Subdivisions of Spheres.- Isotopic Implicit Surface Meshing.- Line Transversals to Disjoint Balls.- Norm Bounds for Ehrhart Polynomial Roots.- Helly-Type Theorems for Line Transversals to Disjoint Unit Balls.- Grid Vertex-Unfolding Orthogonal Polyhedra.- Empty Convex Hexagons in Planar Point Sets.- Affinely Regular Polygons as Extremals of Area Functionals.- Improved Output-Sensitive Snap Rounding.- Generating All Vertices of a Polyhedron Is Hard.- Pure Point Diffractive Substitution Delone Sets Have the Meyer Property.- Metric Combinatorics of Convex Polyhedra: Cut Loci and Nonoverlapping Unfoldings.- Empty Simplices of Polytopes and Graded Betti Numbers.- Rigidity and the Lower Bound Theorem for Doubly Cohen-Macaulay Complexes.- Finding the Homology of Submanifolds with High Confidence from Random Samples.- Odd Crossing Number and Crossing Number Are Not the Same.- Visibility Graphs of Point Sets in the Plane.- Decomposability of Polytopes.- An Inscribing Model for Random Polytopes.- An Optimal-Time Algorithm for Shortest Paths on a Convex Polytope in Three Dimensions.- General-Dimensional Constrained Delaunay and Constrained Regular Triangulations, I: Combinatorial Properties.