Praise for the Third Edition “Researchers of any kind of extremal combinatorics or theoretical
computer science will welcome the new edition of this book.”-MAA Reviews Maintaining a …

Historically, there is a close connection between geometry and optImization. This is
illustrated by methods like the gradient method and the simplex method, which are …

Recently, it became apparent that a large number of the most interesting structures and
phenomena of the world can be described by networks. To develop a mathematical theory of …

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 …

Davenport Schinzel sequences are sequences that do not contain forbidden alternating
subsequences of certain length. They are a powerful combinatorial tool applicable in …

We give a deterministic polynomial time method for finding a set cover in a set system (X, ℜ)
of VC-dimension d such that the size of our cover is at most a factor of O (d log (dc)) from the …

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 …

A complete, self-contained introduction to a powerful and resurging mathematical discipline
Combinatorial Geometry presents and explains with complete proofs some of the most …

A typical range-searching problem has the following form: Pre-process a set S of points in R*
so that the points of S lying inside a query region can be reported or counted quickly. We …

Discrepancy theory is also called the theory of irregularities of distribution. Here are some
typical questions: What is the" most uniform" way of dis tributing n points in the unit square …