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 AMS-IMS-SIAM 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.
Geometric range searching and its relatives by P. K. Agarwal and J. Erickson Deformed products and maximal shadows of polytopes by N. Amenta and G. M. Ziegler Flag complexes, labelled rooted trees, and star shellings by L. J. Billera, C. S. Chan, and N. Liu Discrepancy bounds for geometric set systems with square incidence matrices by B. Chazelle Computational topology by T. K. Dey, H. Edelsbrunner, and S. Guha Recent progress on packing and covering by G. Fejes Toth Acoptic polyhedra by B. Grunbaum A proof of the strict monotone 4-step conjecture by F. Holt and V. Klee Interactions between real algebraic geometry and discrete and computational geometry by I. Itenberg and M.-F. Roy Open problems in the combinatorics of visibility and illumination by J. O'Rourke Halving lines and perfect cross-matchings by J. Pach and J. Solymosi Three-dimensional grid drawings of graphs by J. Pach, T. Thiele, and G. Toth On polygonal covers by M. Pocchiola and G. Vegter The universality theorems for oriented matroids and polytopes by J. Richter-Gebert Periodic and aperiodic tilings of $E^n$ by M. Senechal The early years of computational geometry-A personal memoir by M. I. Shamos Arrangements of surfaces in higher dimensions by M. Sharir Geometric discrepancy theory by J. Spencer Proof of Reay's conjecture on certain positive-dimensional intersections by H. Tverberg Progress in geometric transversal theory by R. Wenger Recent progress on polytopes by G. M. Ziegler Application challenges to computational geometry (CG impact task force report).