Approximate Range Searching In The Absolute Error Model (2007)
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BibTeX
@MISC{Fonseca07approximaterange,
author = {Guilherme Dias da Fonseca},
title = {Approximate Range Searching In The Absolute Error Model},
year = {2007}
}
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Abstract
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 prior work on this problem has focused on the relative error model, where each range shape R is bounded, and points within distance ε · diam(R) of the range’s boundary may or may not be in-cluded. We introduce a different approximation model, called the absolute error model, in which points within distance ε of the range’s boundary may or may not be included, regardless of the diameter of the range. We consider sets of ranges consisting of general convex bodies, axis-aligned rectangles, halfspaces, Euclidean balls, and simplices. We examine a variety of problem formulations, including range searching under general commutative semigroups, idempotent semigroups, groups, range emptiness, and range re-porting. We apply our data structures to several related problems, including range sketching, approximate nearest neighbor searching, exact idempotent range searching, approximate range searching in the data stream model, and
Keyphrases
absolute error model approximate range searching problem formulation range searching computational geometry axis-aligned rectangle general commutative semigroups range emptiness data stream model data structure neighbor searching approximation parameter general convex body exact idempotent range searching several related problem idempotent semigroups different approximation model prior work range shape range sketching approximate range relative error model distance diam
