Selecting distances in the plane


Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Agarwal, PK; Aronov, B; Sharir, M; Suri, S

Published Date

  • May 1, 1993

Published In

Volume / Issue

  • 9 / 5

Start / End Page

  • 495 - 514

Electronic International Standard Serial Number (EISSN)

  • 1432-0541

International Standard Serial Number (ISSN)

  • 0178-4617

Digital Object Identifier (DOI)

  • 10.1007/BF01187037

Citation Source

  • Scopus