Contemporary Mathematics 1999; 463 pp; softcover Volume: 223 ISBN10: 0821806742 ISBN13: 9780821806746 List Price: US$120 Member Price: US$96 Order Code: CONM/223
 This volume is a collection of refereed expository and research articles in discrete and computational geometry written by leaders in the field. Articles are based on invited talks presented at the AMSIMSSIAM Summer Research Conference, "Discrete and Computational Geometry: Ten Years Later", held in 1996 at Mt. Holyoke College (So. Hadley, MA). Topics addressed range from tilings, polyhedra, and arrangements to computational topology and visibility problems. Included are papers on the interaction between real algebraic geometry and discrete and computational geometry, as well as on linear programming and geometric discrepancy theory. Readership Graduate students and research mathematicians working in discrete and computational geometry; applied workers using geometric methods and results, such as computer graphics and design. Table of Contents  P. K. Agarwal and J. Erickson  Geometric range searching and its relatives
 N. Amenta and G. M. Ziegler  Deformed products and maximal shadows of polytopes
 L. J. Billera, C. S. Chan, and N. Liu  Flag complexes, labelled rooted trees, and star shellings
 B. Chazelle  Discrepancy bounds for geometric set systems with square incidence matrices
 T. K. Dey, H. Edelsbrunner, and S. Guha  Computational topology
 G. Fejes Tóth  Recent progress on packing and covering
 B. Grünbaum  Acoptic polyhedra
 F. Holt and V. Klee  A proof of the strict monotone 4step conjecture
 I. Itenberg and M.F. Roy  Interactions between real algebraic geometry and discrete and computational geometry
 J. O'Rourke  Open problems in the combinatorics of visibility and illumination
 J. Pach and J. Solymosi  Halving lines and perfect crossmatchings
 J. Pach, T. Thiele, and G. Tóth  Threedimensional grid drawings of graphs
 M. Pocchiola and G. Vegter  On polygonal covers
 J. RichterGebert  The universality theorems for oriented matroids and polytopes
 M. Senechal  Periodic and aperiodic tilings of \(E^n\)
 M. I. Shamos  The early years of computational geometryA personal memoir
 M. Sharir  Arrangements of surfaces in higher dimensions
 J. Spencer  Geometric discrepancy theory
 H. Tverberg  Proof of Reay's conjecture on certain positivedimensional intersections
 R. Wenger  Progress in geometric transversal theory
 G. M. Ziegler  Recent progress on polytopes
 Application challenges to computational geometry (CG impact task force report)
