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Publications [#235575] of Pankaj K. Agarwal

Papers Published

  1. Agarwal, PK; Aronov, B; Sharir, M; Suri, S, Selecting distances in the plane, Algorithmica, vol. 9 no. 5 (1993), pp. 495-514, ISSN 0178-4617 [doi]
    (last updated on 2018/11/18)

    We present 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 [Mel]. The expected running time of our algorithm is O(n4/3 log8/3n). The algorithm can also be made deterministic, using a more complicated technique, with only a slight increase in its running time. A much simpler deterministic version of our procedure runs in time O(n3/2 log5/2n). All versions improve the previously best-known upper bound of O(@#@ n9/5 log4/5n) by Chazelle [Ch]. A simple O(n log n)-time algorithm for computing an approximation of the median distance is also presented. © 1993 Springer-Verlag New York Inc.
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