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Discrete and Computational Geometry: Papers from the DIMACS Special Year
 
A co-publication of the AMS, DIMACS, and Association for Computing Machinery
Discrete and Computational Geometry: Papers from the DIMACS Special Year
Hardcover ISBN:  978-0-8218-6595-8
Product Code:  DIMACS/6
List Price: $95.00
MAA Member Price: $85.50
AMS Member Price: $76.00
eBook ISBN:  978-1-4704-3964-4
Product Code:  DIMACS/6.E
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
Hardcover ISBN:  978-0-8218-6595-8
eBook: ISBN:  978-1-4704-3964-4
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
Discrete and Computational Geometry: Papers from the DIMACS Special Year
Click above image for expanded view
Discrete and Computational Geometry: Papers from the DIMACS Special Year
A co-publication of the AMS, DIMACS, and Association for Computing Machinery
Hardcover ISBN:  978-0-8218-6595-8
Product Code:  DIMACS/6
List Price: $95.00
MAA Member Price: $85.50
AMS Member Price: $76.00
eBook ISBN:  978-1-4704-3964-4
Product Code:  DIMACS/6.E
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
Hardcover ISBN:  978-0-8218-6595-8
eBook ISBN:  978-1-4704-3964-4
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 Details
     
     
    DIMACS - Series in Discrete Mathematics and Theoretical Computer Science
    Volume: 61991; 378 pp
    MSC: 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.

    Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1–7 were co-published 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
    • Wu-Ritt 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
    • Rational-function-valued valuations on polyhedra
    • Winding numbers and the generalized lower-bound 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 double-lattice 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 Katchalski-Lewis conjecture on partial transversals for translates
    • Invariant-theoretic computation in projective geometry
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 61991; 378 pp
MSC: 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.

Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1–7 were co-published 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
  • Wu-Ritt 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
  • Rational-function-valued valuations on polyhedra
  • Winding numbers and the generalized lower-bound 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 double-lattice 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 Katchalski-Lewis conjecture on partial transversals for translates
  • Invariant-theoretic computation in projective geometry
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.