@article{4048,
abstract = {Given a sequence of n points that form the vertices of a simple polygon, we show that determining a closest pair requires OMEGA(n log n) time in the algebraic decision tree model. Together with the well-known O(n log n) upper bound for finding a closest pair, this settles an open problem of Lee and Preparata. We also extend this O(n log n) upper bound to the following problem: Given a collection of sets with a total of n points in the plane, find for each point a closest neighbor that does not belong to the same set.},
author = {Aggarwal, Alok and Herbert Edelsbrunner and Raghavan, Prabhakar and Tiwari, Prasoon},
journal = {Information Processing Letters},
number = {1},
pages = {55 -- 60},
publisher = {Elsevier},
title = {{Optimal time bounds for some proximity problems in the plane}},
doi = {10.1016/0020-0190(92)90133-G},
volume = {42},
year = {1992},
}