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Hardcover ISBN:  9780821865958 
Product Code:  DIMACS/6 
List Price:  $95.00 
MAA Member Price:  $85.50 
AMS Member Price:  $76.00 
eBook ISBN:  9781470439644 
Product Code:  DIMACS/6.E 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 
Hardcover ISBN:  9780821865958 
eBook ISBN:  9781470439644 
Product Code:  DIMACS/6.B 
List Price:  $184.00 $139.50 
MAA Member Price:  $165.60 $125.55 
AMS Member Price:  $147.20 $111.60 

Book DetailsDIMACS  Series in Discrete Mathematics and Theoretical Computer ScienceVolume: 6; 1991; 378 ppMSC: Primary 03; 05; 12; 13; 14; 15; 32; 51; 52; 57; 68
The first DIMACS special year, held during 1989–1990, was devoted to discrete and computational geometry. 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 results of the workshops and the special year activities. Containing both survey articles and research papers, this collection presents an excellent overview of 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 stimulation between the two disciplines.
Copublished with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1–7 were copublished with the Association for Computer Machinery (ACM).

Table of Contents

Chapters

Geometric partitioning and its applications

On the convex hull of the integer points in a disc

Horizon theorems for lines and polygons

On the perimeter of a point set in the plane

Lines in space—A collection of results

Singularities of minimal surfaces and networks and related extremal problems in Minkowski space

WuRitt characteristic sets and their complexity

Algorithms in real algebraic geometry and applications to computational geometry

Ehrhart polynomials of convex polytopes, $h$vectors of simplicial complexes, and nonsingular projective toric varieties

Unimodular fans, linear codes, and toric manifolds

New results for simplicial spherical polytopes

Rationalfunctionvalued valuations on polyhedra

Winding numbers and the generalized lowerbound conjecture

Computing the center of planar point sets

Finite quotients of infinite universal polytopes

The universality theorem on the oriented matroid stratification of the space of real matrices

The densest doublelattice packing of a convex polygon

Arrangements in topology

Notes on geometric graph theory

Recent progress on the complexity of the decision problem for the reals

Sweeping arrangements of curves

On geometric permutations and the KatchalskiLewis conjecture on partial transversals for translates

Invarianttheoretic computation in projective geometry


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The first DIMACS special year, held during 1989–1990, was devoted to discrete and computational geometry. 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 results of the workshops and the special year activities. Containing both survey articles and research papers, this collection presents an excellent overview of 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 stimulation between the two disciplines.
Copublished with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1–7 were copublished with the Association for Computer Machinery (ACM).

Chapters

Geometric partitioning and its applications

On the convex hull of the integer points in a disc

Horizon theorems for lines and polygons

On the perimeter of a point set in the plane

Lines in space—A collection of results

Singularities of minimal surfaces and networks and related extremal problems in Minkowski space

WuRitt characteristic sets and their complexity

Algorithms in real algebraic geometry and applications to computational geometry

Ehrhart polynomials of convex polytopes, $h$vectors of simplicial complexes, and nonsingular projective toric varieties

Unimodular fans, linear codes, and toric manifolds

New results for simplicial spherical polytopes

Rationalfunctionvalued valuations on polyhedra

Winding numbers and the generalized lowerbound conjecture

Computing the center of planar point sets

Finite quotients of infinite universal polytopes

The universality theorem on the oriented matroid stratification of the space of real matrices

The densest doublelattice packing of a convex polygon

Arrangements in topology

Notes on geometric graph theory

Recent progress on the complexity of the decision problem for the reals

Sweeping arrangements of curves

On geometric permutations and the KatchalskiLewis conjecture on partial transversals for translates

Invarianttheoretic computation in projective geometry