Computational geometry is concerned with the design and analysis of algorithms for
geometrical problems. In addition, other more practically oriented, areas of computer …

It has often been asserted that since hierarchical clustering algorithms require pairwise
interobject proximities, the complexity of these clustering procedures is at least O (N 2) …

An adaptive method based on the idea of multiple component grids for the solution of
hyperbolic partial differential equations using finite difference techniques is presented …

We explore the effect of dimensionality on the “nearest neighbor” problem. We show that
under a broad set of conditions (much broader than independent and identically distributed …

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 …

We present a transformation that can be used to compute Voronoi diagrams with a
sweepline technique. The transformation is used to obtain simple algorithms for computing …

This paper surveys locally weighted learning, a form of lazy learning and memory-based
learning, and focuses on locally weighted linear regression. The survey discusses distance …

The problem of searching the elements of a set that are close to a given query element
under some similarity criterion has a vast number of applications in many branches of …

The topic of this chapter, Voronoi diagrams, di ers from other areas of computational
geometry, in that its origin dates back to the 17th century. In his book on the principles of …

Photon map**, an extension of ray tracing, makes it possible to efficiently simulate global
illumination in complex scenes. Photon map** can simulate caustics (focused light, like …