Math @ Duke

Publications [#235384] of Pankaj K. Agarwal
Papers Published
 Agarwal, PK; Edelsbrunner, H; Schwarzkopf, O; Welzl, E, Euclidean minimum spanning trees and bichromatic closest pairs,
Discrete & Computational Geometry, vol. 6 no. 1
(1991),
pp. 407422, ISSN 01795376 [doi]
(last updated on 2017/12/12)
Abstract: We present an algorithm to compute a Euclidean minimum spanning tree of a given set S of N points in E d in time O(F d (N,N) log d N), where F d (n,m) is the time required to compute a bichromatic closest pair among n red and m green points in E d . If F d (N,N)=Ω(N 1+ε), for some fixed e{open}>0, then the running time improves to O(F d (N,N)). Furthermore, we describe a randomized algorithm to compute a bichromatic closest pair in expected time O((nm log n log m)2/3+m log2 n+n log2 m) in E 3, which yields an O(N 4/3 log4/3 N) expected time, algorithm for computing a Euclidean minimum spanning tree of N points in E 3. In d≥4 dimensions we obtain expected time O((nm)11/([d/2]+1)+ε+m log n+n log m) for the bichromatic closest pair problem and O(N 22/([d/2]+1)ε) for the Euclidean minimum spanning tree problem, for any positive e{open}. © 1991 SpringerVerlag New York Inc.


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