Range Searching Range Searching

Geometric Range Searching and Its Relatives

About ten years ago, the eld of range searching, especially simplex range searching, was wide open. At that time, neither e cient algorithms nor nontrivial lower bounds were known for most range-searching problems. A series of papers by Haussler and Welzl [161], Clarkson [88, 89], and Clarkson and Shor [92] not only marked the beginning of a new chapter in geometric searching, but also revitali...

Geometric Range Searching and Its Relatives Geometric Range Searching and Its Relatives

Title of Dissertation : Approximate Range Searching In The Absolute Error Model Guilherme

Title of Dissertation: Approximate Range Searching In The Absolute Error Model Guilherme Dias da Fonseca, Doctor of Philosophy, 2007 Dissertation directed by: Professor David M. Mount Department of Computer Science Range searching is a well known problem in computational geometry. We consider this problem in the context of approximation, where an approximation parameter ε > 0 is provided. Most ...

Invited Lecture: On Approximate Range Searching - or - Get in Shape; Round is a Good Choice

Range searching is among the most fundamental and well-studied problems in computational geometry. Given an n-element point set in R, the problem is to preprocess the points so that the total weight, or generally the semigroup sum, of the points lying within a given query range η can be determined quickly. Years of research have resulted in nearly matching upper and lower bounds for many formul...

Simplex Range Searching and Its Variants: A Review∗

A central problem in computational geometry, range searching arises in many applications, and numerous geometric problems can be formulated in terms of range searching. A typical range-searching problem has the following form. Let S be a set of n points in Rd, and let R be a family of subsets of Rd; elements of R are called ranges. Preprocess S into a data structure so that for a query range γ ...