New Trends in Discrete and Computational Geometry

The most important new developments in discrete and computational geometry are summarized in this book. Special emphasis is put on those questions where the interaction between the two disciplines is the strongest. Concise and clear in style, this book introduces the most efficient combinatorial, probabilistic and topological methods that can be used to design effective geometric algorithms for motion planning, robotics, scene analysis, computer-aided design, etc. Most of the methods and results discussed in the book have not appeared in any previously published monograph. In particular, this book contains the first systematic treatment of epsilon-nets, geometric transversal theory, partitions of Euclidean spaces and a general method for the analysis of randomized geometric algorithms. The chapters are self-con- tained surveys written by leading experts in the field. The book will be used by researchers, graduate students, and engineers interested in applications.