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Discrete and Computational Geometry: Papers from the DIMACS Special Year
Edited by: Jacob E. Goodman, Richard Pollack, and William Steiger
A co-publication of the AMS, DIMACS, and Association for Computing Machinery.
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DIMACS: Series in Discrete Mathematics and Theoretical Computer Science
1991; 378 pp; hardcover
Volume: 6
ISBN-10: 0-8218-6595-1
ISBN-13: 978-0-8218-6595-8
List Price: US$80
Member Price: US$64
Order Code: DIMACS/6
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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.

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

  • P. K. Agarwal -- Geometric partitioning and its applications
  • A. Balog and I. Bárány -- On the convex hull of the integer points in a disc
  • M. Bern, D. Eppstein, P. Plassmann, and F. Yao -- Horizon theorems for lines and polygons
  • V. Capolyeas and J. Pach -- On the perimeter of a point set in the plane
  • H. Edelsbrunner -- Lines in space--A collection of results
  • Z. Füredi, J. C. Lagarias, and F. Morgan -- Singularities of minimal surfaces and networks and related extremal problems in Minkowski space
  • G. Gallo and B. Mishra -- Wu-Ritt characteristic sets and their complexity
  • J. Heintz, T. Recio, and M.-F. Roy -- Algorithms in real algebraic geometry and applications to computational geometry
  • T. Hibi -- Ehrhart polynomials of convex polytopes, \(h\)-vectors of simplicial complexes, and nonsingular projective toric varieties
  • P. Kleinschmidt, N. Schwartz, and B. Sturmfels -- Unimodular fans, linear codes, and toric manifolds
  • P. Kleinschmidt and Z. Smilansky -- New results for simplicial spherical polytopes
  • J. Lawrence -- Rational-function-valued valuations on polyhedra
  • C. W. Lee -- Winding numbers and the generalized lower-bound conjecture
  • J. Matoušek -- Computing the center of planar point sets
  • P. McMullen and E. Schulte -- Finite quotients of infinite universal polytopes
  • N. Mnëv -- The universality theorem on the oriented matroid stratification of the space of real matrices
  • D. M. Mount -- The densest double-lattice packing of a convex polygon
  • P. Orlik -- Arrangements in topology
  • J. Pach -- Notes on geometric graph theory
  • J. Renegar -- Recent progress on the complexity of the decision problem for the reals
  • J. Snoeyink and J. Hershberger -- Sweeping arrangements of curves
  • H. Tverberg -- On geometric permutations and the Katchalski-Lewis conjecture on partial transversals for translates
  • N. L. White -- Invariant-theoretic computation in projective geometry
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