Well-separated pair decomposition in linear time?

Authors:
Timothy M. Chan
Affiliations:
School of Computer Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Venue:
Information Processing Letters
Year:
2008

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Abstract

Given a point set in a fixed dimension, we note that a well-separated pair decomposition can be found in linear time if we assume that the ratio of the farthest pair distance to the closest pair distance is polynomially bounded. Many consequences follow; for example, we can construct spanners or solve the all-nearest-neighbors problem in linear time (under the same assumption), and we compute an approximate Euclidean minimum spanning tree in linear time (without any assumption).