Discrete and Computational Geometry

Table of Contents

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   Book Overview
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   Chapter 1 On the Complexity of Many Faces in Arrangements of Pseudo-Segments and Circles
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   Chapter 2 Polyhedral Cones of Magic Cubes and Squares
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   Chapter 3 Congruent Dudeney Dissections of Triangles and Convex Quadrilaterals – All Hinge Points Interior to the Sides of the Polygons
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   Chapter 4 Computing the Hausdorff Distance of Geometric Patterns and Shapes
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   Chapter 5 A Sum of Squares Theorem for Visibility Complexes and Applications
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   Chapter 6 On the Reflexivity of Point Sets
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   Chapter 7 Geometric Permutations of Large Families of Translates
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   Chapter 8 Integer Points in Rotating Convex Bodies
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    Chapter 9 Complex Matroids Phirotopes and Their Realizations in Rank 2
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    Chapter 10 Covering the Sphere by Equal Spherical Balls
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    Chapter 11 Lower Bounds for High Dimensional Nearest Neighbor Search and Related Problems
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    Chapter 12 A Turán-type Extremal Theory of Convex Geometric Graphs
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    Chapter 13 On the Inapproximability of Polynomial-programming, the Geometry of Stable Sets, and the Power of Relaxation
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    Chapter 14 A Lower Bound on the Complexity of Approximate Nearest-Neighbor Searching on the Hamming Cube
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    Chapter 15 Detecting Undersampling in Surface Reconstruction
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    Chapter 16 A Survey of the Hadwiger-Debrunner ( p, q )-problem
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    Chapter 17 Surface Reconstruction by Wrapping Finite Sets in Space
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    Chapter 18 Infeasibility of Systems of Halfspaces
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    Chapter 19 Combinatorial Generation of Small Point Configurations and Hyperplane Arrangements
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    Chapter 20 Relative Closure and the Complexity of Pfaffian Elimination
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    Chapter 21 Are Your Polyhedra the Same as My Polyhedra?
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    Chapter 22 Some Algorithms Arising in the Proof of the Kepler Conjecture
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    Chapter 23 The Minimal Number of Triangles Needed to Span a Polygon Embedded in ℝ d
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    Chapter 24 Jacobi Decomposition and Eigenvalues of Symmetric Matrices
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    Chapter 25 Discrete Geometry on Red and Blue Points in the Plane — A Survey —
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    Chapter 26 Configurations with Rational Angles and Trigonometric Diophantine Equations
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    Chapter 27 Reconstructing Sets From Interpoint Distances
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    Chapter 28 Dense Packings of Congruent Circles in Rectangles with a Variable Aspect Ratio
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    Chapter 29 Colorings and Homomorphisms of Minor Closed Classes
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    Chapter 30 Conflict-free Colorings
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    Chapter 31 New Complexity Bounds for Cylindrical Decompositions of Sub-Pfaffian Sets
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    Chapter 32 Note on the Chromatic Number of the Space
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    Chapter 33 Expansive Motions and the Polytope of Pointed Pseudo-Triangulations
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    Chapter 34 Some Recent Quantitative and Algorithmic Results in Real Algebraic Geometry
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    Chapter 35 A Discrete Isoperimetric Inequality and Its Application to Sphere Packings
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    Chapter 36 On the Number of Maximal Regular Simplices Determined by n Points in Rd
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    Chapter 37 Balanced Lines, Halving Triangles, and the Generalized Lower Bound Theorem
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    Chapter 38 Quantizing Using Lattice Intersections
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    Chapter 39 Note on a Generalization of Roth’s Theorem
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    Chapter 40 Arrangements, Equivariant Maps and Partitions of Measures by k -Fans
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    Chapter 41 Qualitative Infinite Version of Erdős’ Problem About Empty Polygons