Well-separated pair decomposition in linear time?
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 in approximate Euclidean minimum spanning tree in linear time (Without any assumption). (C) 2008 Elsevier B.V. All rights reserved.
computational geometry approximation algorithms quadtrees