Combinatorial and Computational Geometry

By: Jacob Eli Goodman (Editor), Janos Pach (Editor), Emo Welzl (Editor), Silvio Levy (Editor)

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Hardcover | 8 August 2005

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630 Pages

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23.39 x 15.6 x 3.51

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During the past few decades, the gradual merger of Discrete Geometry and the newer discipline of Computational Geometry has provided enormous impetus to mathematicians and computer scientists interested in geometric problems. This volume, which contains 32 papers on a broad range of topics of current interest in the field, is an outgrowth of that synergism. It includes surveys and research articles exploring geometric arrangements, polytopes, packing, covering, discrete convexity, geometric algorithms and their complexity, and the combinatorial complexity of geometric objects, particularly in low dimension. There are points of contact with many applied areas such as mathematical programming, visibility problems, kinetic data structures, and biochemistry, as well as with algebraic topology, geometric probability, real algebraic geometry, and combinatorics.

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Non-Fiction Computing & I.T.Business Applications Mathematical & Statistical Software Mathematics Geometry Reference, Information & Interdisciplinary Subjects

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Published: 2nd June 2011

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Preface	p. xi
Geometric Approximation via Coresets	p. 1
Applications of Graph and Hypergraph Theory in Geometry	p. 31
Convex Geometry of Orbits	p. 51
The Hadwiger Transversal Theorem for Pseudolines	p. 79
Betti Number Bounds, Applications and Algorithms	p. 87
Shelling and the h-Vector of the (Extra)ordinary Polytope	p. 97
On the Number of Mutually Touching Cylinders	p. 121
Edge-Antipodal 3-Polytopes	p. 129
A Conformal Energy for Simplicial Surfaces	p. 135
On the Size of Higher-Dimensional Triangulations	p. 147
The Carpenter's Ruler Folding Problem	p. 155
A Survey of Folding and Unfolding in Computational Geometry	p. 167
On the Rank of a Tropical Matrix	p. 213
The Geometry of Biomolecular Solvation	p. 243
Inequalities for Zonotopes	p. 277
Quasiconvex Programming	p. 287
De Concini-Procesi Wonderful Arrangement Models: A Discrete Geometer's Point of View	p. 333
Thinnest Covering of a Circle by Eight, Nine, or Ten Congruent Circles	p. 361
On the Complexity of Visibility Problems with Moving Viewpoints	p. 377
Cylindrical Partitions of Convex Bodies	p. 399
Tropical Halfspaces	p. 409
Two Proofs for Sylvester's Problem Using an Allowable Sequence of Permutations	p. 433
A Comparison of Five Implementations of 3D Delaunay Tessellation	p. 439
The Bernstein Basis and Real Root Isolation	p. 459
Extremal Problems Related to the Sylvester-Gallai Theorem	p. 479
A Long Noncrossing Path Among Disjoint Segments in the Plane	p. 495
On a Generalization of Schonhardt's Polyhedron	p. 501
On Hadwiger Numbers of Direct Products of Convex Bodies	p. 517
Binary Space Partitions: Recent Developments	p. 529
The Erdos-Szekeres Theorem: Upper Bounds and Related Results	p. 557
On the Pair-Crossing Number	p. 569
Geometric Random Walks: A Survey	p. 577
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Combinatorial and Computational Geometry

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