@article{Shamos1975ClosestpointP,
title={Closest-point problems},
author={Michael Ian Shamos and Dan Hoey},
journal={16th Annual Symposium on Foundations of Computer Science (sfcs 1975)},
year={1975},
pages={151-162}
}

A number of seemingly unrelated problems involving the proximity of N points in the plane are studied, such as finding a Euclidean minimum spanning tree, the smallest circle enclosing the set, k nearest and farthest neighbors, the two closest points, and a proper straight-line triangulation. For most of the problems considered a lower bound of O(N log N) is shown. For all of them the best currently-known upper bound is O(N2) or worse. The purpose of this paper is to introduce a single geometricâ€¦Â CONTINUE READING