Math @ Duke

Publications [#235561] of Pankaj K. Agarwal
Papers Published
 Agarwal, PK; Aronov, B; Sharir, M; Suri, S, Selecting distances in the plane,
in Sixth Annual Symposium on Computational Geometry
(1990),
pp. 321331
(last updated on 2017/12/16)
Abstract: We describe a randomized algorithm for computing the kth smallest distance in a set of n points in the plane, based on the parametric search technique of Megiddo. The expected running time of our algorithm is O(n4/3 log8/3 n). A deterministic version of our procedure runs in time O(n3/2 log5/2 n). Both versions improve the previously best known upper bound of O(n9/5 log4/5 n) by Chazelle. A simple O(n log n) time algorithm for computing an approximation of the median distance is also presented.


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