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Applied Geometry and Discrete Mathematics: The Victor Klee Festschrift
Edited by: Peter Gritzmann and Bernd Sturmfels
A co-publication of the AMS, DIMACS, and Association for Computing Machinery.

DIMACS: Series in Discrete Mathematics and Theoretical Computer Science
1991; 608 pp; hardcover
Volume: 4
ISBN-10: 0-8218-6593-5
ISBN-13: 978-0-8218-6593-4
List Price: US$144
Member Price: US$115.20
Order Code: DIMACS/4
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This volume, published jointly with the Association for Computing Machinery, comprises a collection of research articles celebrating the occasion of Victor Klee's sixty-fifth birthday in September 1990. During his long career, Klee has made contributions to a wide variety of areas, such as discrete and computational geometry, convexity, combinatorics, graph theory, functional analysis, mathematical programming and optimization, and theoretical computer science. In addition, Klee made important contributions to mathematics education, mathematical methods in economics and the decision sciences, applications of discrete mathematics in the biological and social sciences, and the transfer of knowledge from applied mathematics to industry.

In honor of Klee's achievements, this volume presents more than forty papers on topics related to Klee's research. While the majority of the papers are research articles, a number of survey articles are also included. Mirroring the breadth of Klee's mathematical contributions, this book shows how different branches of mathematics interact. It is a fitting tribute to one of the foremost leaders in discrete mathematics.

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).


"The reader of this excellent collection of papers will have the opportunity to be exposed to every current trend in concrete geometry. Highly recommended."

-- The Bulletin of Mathematics Books and Computer Software

Table of Contents

  • H. Achatz, P. Kleinschmidt, and K. Paparrizos -- A dual forest algorithm for the assignment problem
  • J. Ashley, B. Grünbaum, G. C. Shephard, and W. Stromquist -- Self-duality groups and ranks of self-dualities
  • I. Bárány, J. E. Goodman, and R. Pollack -- Do projections go to infinity?
  • D. W. Barnette -- The minimal projective plane polyhedral maps
  • A. Bezdek and W. Kuperberg -- Packing Euclidean space with congruent cylinders and with congruent ellipsoids
  • A. Björner and G. Kalai -- Extended Euler-Poincaré relations for cell complexes
  • K. H. Borgwardt, N. Gaffke, M. Jünger, and G. Reinelt -- Computing the convex hull in the Euclidean plane in linear expected time
  • M. Breen -- Measures of \(F\)-stars in finitely starlike sets
  • R. A. Brualdi and B. L. Shader -- On sign-nonsingular matrices and the conversion of the permanent into the determinant
  • E. Cohen and N. Megiddo -- Recognizing properties of periodic graphs
  • R. Connelly -- On generic global rigidity
  • H. S. M. Coxeter and G. C. Shephard -- Some regular maps and their polyhedral realizations
  • L. Dalla and D. G. Larman -- Volumes of a random polytope in a convex set
  • B. V. Dekster -- Bodies of constant width in Riemannian manifolds and spaces of constant curvature
  • D. DeTemple, J. Robertson, and G. Wood -- Uniquely remotal hulls
  • M. Deza, V. P. Grishukhin, and M. Laurent -- The symmetries of the cut polytope and of some relatives
  • M. Deza, M. Grötschel, and M. Laurent -- Complete descriptions of small multicut polytopes
  • H. Edelsbrunner and M. Sharir -- A hyperplane incidence problem with applications to counting distances
  • P. Erdős, E. Makai, J. Pach, and J. Spencer -- Gaps in difference sets, and the graph of nearly equal distances
  • G. F. Tóth and L. F. Tóth -- Remarks on \(5\)-neighbor packings and coverings with circles
  • P. Filliman -- Symmetric solutions to isoperimetric problems for polytopes
  • A. A. Goldstein -- A global Newton method
  • P. M. Gruber -- Volume approximation of convex bodies by circumscribed polytopes
  • H. Harborth and L. Piepmeyer -- Points sets with small integral distances
  • E. Heil -- Convex minimizers of variational problems
  • P. Hilfinger, E. L. Lawler, and G. Rote -- Flattening a rooted tree
  • R. Horst and H. Tuy -- The geometric complementarity problem and transcending stationarity in global optimization
  • T. C. Hu and A. B. Kahng -- Every tree is graceful (but some are more graceful than others)
  • C. R. Johnson and J. Maybee -- Qualitative analysis of Schur complements
  • M. J. Kaiser, T. L. Morin, and T. B. Trafalis -- Centers and invariant points of convex bodies
  • G. Kalai -- The diameter of graphs of convex polytopes and \(f\)-vector theory
  • L. M. Kelly -- Multiply perspective simplices, Desmic triads and the Edelstein Theorems
  • W. Kühnel and Ch. Schulz -- Submanifolds of the cube
  • J. Lawrence -- Finite unions of closed subgroups of the \(n\)-dimensional torus
  • C. W. Lee -- Regular triangulations of convex polytopes
  • E. Makai, Jr. and H. Martini -- On the number of antipodal or strictly antipodal pairs of points in finite subsets of \(\mathbb R^d\)
  • J.-E. Martínez-Legaz and I. Singer -- Multi-order convexity
  • M. Rosenfeld -- Almost orthogonal lines in \(E^d\)
  • E. Schulte and A. I. Weiss -- Chiral polytopes
  • R. Seidel -- Exact upper bounds for the number of faces in \(d\)-dimensional Voronoi diagrams
  • P. W. Shor -- Stretchability of pseudolines is NP-hard
  • R. P. Stanley -- A zonotope associated with graphical degree sequences
  • K. Sundaresan -- Geometry of spaces of homogeneous polynomials on Banach lattices
  • W. Whiteley -- The combinatorics of bivariate splines
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