We review the recent progress in the design of efficient algorithms for various problems in
geometric optimization. We present several techniques used to attack these problems, such …

In geometric range searching, algorithmic problems of the following type are considered.
Given an n-point set P in the plane, build a data structure so that, given a query triangle R …

The nearest neighbor problem is the follolving: Given a set of n points P=(PI,..., p,} in some
metric space X, preprocess P so as to efficiently answer queries which require finding bhe …

Consider a set of S of n data points in real d-dimensional space, Rd, where distances are
measured using any Minkowski metric. In nearest neighbor searching, we preprocess S into …

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

We address the problem of designing data structures that allow efficient search for
approximate nearest neighbors. More specifically, given a database consisting of a set of …

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 …

This handbook provides an up-to-date compendium of fundamental computer science
topics, techniques, and applications. Along with updating and revising many of the existing …

Representing data as points in a high-dimensional space, so as to use geometric methods
for indexing, is an algorithmic technique with a wide array of uses. It is central to a number of …

Global illumination research aiming at the photo-realistic image synthesis pushes forward
research in computer graphics as a whole. The computation of visually plausible images is …