Suppose we are simulating a collection of continuously moving bodies, rigid or deformable,
whose instantaneous motion follows known laws. As the simulation proceeds, we are …

This well-accepted introduction to computational geometry is a textbook for high-level
undergraduate and low-level graduate courses. The focus is on algorithms and hence the …

This book is primarily a textbook introduction to various areas of discrete geometry. In each
area, it explains several key results and methods, in an accessible and concrete manner. It …

Delineating the tremendous growth in this area, the Handbook of Approximation Algorithms
and Metaheuristics covers fundamental, theoretical topics as well as advanced, practical …

Exact algorithms for dealing with geometric objects are complicated, hard to implement in
practice, and slow. Over the last 20 years a theory of geometric approximation algorithms …

This paper surveys how the concept of crossing number, which used to be familiar only to a
limited group of specialists, emerges as a significant graph parameter. This paper has dual …

Although modern location theory is now more than 90 years old, the focus of researchers in
this area has been mainly problem oriented. However, a common theory, which keeps the …

We prove an O (n (k+ 1) 1/3) upper bound for planar k-sets. This is the first considerable
improvement on this bound after its early solution approximately 27 years ago. Our proof …

The arrangement of a finite collection of geometric objects is the decomposition of the space
into connected cells induced by them. We survey combinatorial and algorithmic properties of …

Given a finite collection S of geometric objects such as hyperplanes or spheres in Rd, the
arrangement A (S) is the decomposition of Rd into connected open cells of dimensions 0 …