Discrete and Computational Geometry: Papers from the DIMACS Special Year

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Jacob E. Goodman, Richard D. Pollack, William L. Steiger
American Mathematical Soc., Jan 1, 1991 - Mathematics - 378 pages
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The first DIMACS special year, held during 1989-1990, was devoted to discrete and computational geometry. More than 200 scientists, both long- and short-term visitors, came to DIMACS to participate in the special year activities. Among the highlights were six workshops at Rutgers and Princeton Universities that defined the focus for much of the special year. The workshops addressed the following topics: geometric complexity, probabilistic methods in discrete and computational geometry, polytopes and convex sets, arrangements, and algebraic and practical issues in geometric computation. This volume presents some of the results growing out of the workshops and the special year activities. Containing both survey articles and research papers, this collection presents an excellent overview of significant recent progress in discrete and computational geometry. The diversity of these papers demonstrate how geometry continues to provide a vital source of ideas in theoretical computer science and discrete mathematics as well as fertile ground for interaction and simulation between the two disciplines.
 

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Contents

Geometric Partitioning and its Applications
1
On the Convex Hull of the Integer Points in a Disc
39
Horizon Theorems for Lines and Polygons
45
On the Perimeter of a Point Set in the Plane
67
Lines in SpaceA Collection of Results
77
Singularities of Minimal Surfaces and Networks and Related Extremal
95
WuRitt Characteristic Sets and Their Complexity
111
Algorithms in Real Algebraic Geometry and Applications
136
Winding Numbers and the Generalized LowerBound Conjecture
209
Computing the Center of Planar Point Sets
221
Finite Quotients of Infinite Universal Polytopes
231
The Universality Theorem on the Oriented Matroid Stratification
237
The Densest DoubleLattice Packing of a Convex Polygon
245
Arrangements in Topology
263
Notes on Geometric Graph Theory
273
Recent Progress on the Complexity of the Decision Problem for
287

Ehrhart Polynomials of Convex Polytopes AVectors of Simplicial
165
Unimodular Fans Linear Codes and Toric Manifolds
179
New Results for Simplicial Spherical Polytopes
187
Rationalfunctionvalued Valuations on Polyhedra
199
Sweeping Arrangements of Curves
309
On Geometric Permutations and the KatchalskiLewis Conjecture
351
InvariantTheoretic Computation in Projective Geometry
363
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