Range Searching

Authored by: Pankaj K. Agarwal

Discrete and Computational Geometry

Print publication date:  April  2004
Online publication date:  April  2004

Print ISBN: 9781584883012
eBook ISBN: 9781420035315
Adobe ISBN:


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Range searching is one of the central problems in computational geometry, because it arises in many applications and a variety of geometric problems can be formulated as range-searching problems. A typical range-searching problem has the following form. Let S be a set of n points in ? d , and let R be a family of subsets of ? d ; elements of R are called ranges . We wish to preprocess S into a data structure, so that for a query range ?, the points in S ∩ ? can be reported or counted efficiently. Typical examples of ranges include rectangles, halfspaces, simplices, and balls. If we are only interested in answering a single query, it can be done in linear time, using linear space, by simply checking each point of S whether it lies in the query range. However, most of the applications call for querying the same set S several times (perhaps with periodic insertions and deletions), in which case we would like to answer a query faster by preprocessing S into a data structure.

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