Optimal Time Bounds for Some Proximity Problems in the Plane

@article{Aggarwal1992OptimalTB,
title={Optimal Time Bounds for Some Proximity Problems in the Plane},
author={Alok Aggarwal and Herbert Edelsbrunner and Prabhakar Raghavan and Prasoon Tiwari},
journal={Inf. Process. Lett.},
year={1992},
volume={42},
pages={55-60}
}

Aggarwal, A., H. Edelsbrunner, P. Raghavan and P. Tiwari, Optimal time bounds for some proximity problems in the plane, Information Processing Letters 42 (1992) 55-60. Given a sequence of n points that form the vertices of a simple polygon, we show that determining a closest pair requires R(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… CONTINUE READING