TY - CONF
AB - We present an algorithm to compute a Euclidean minimum spanning tree of a given set S of n points in Ed in time O(Td(N, N) logd N), where Td(n, m) is the time required to compute a bichromatic closest pair among n red and m blue points in Ed. If Td(N, N) = Ω(N1+ε), for some fixed ε > 0, then the running time improves to O(Td(N, N)). Furthermore, we describe a randomized algorithm to compute a bichromatic closets pair in expected time O((nm log n log m)2/3+m log2 n + n log2 m) in E3, which yields an O(N4/3log4/3 N) expected time algorithm for computing a Euclidean minimum spanning tree of N points in E3.
AU - Agarwal, Pankaj
AU - Edelsbrunner, Herbert
AU - Schwarzkopf, Otfried
AU - Welzl, Emo
ID - 4076
SN - 978-0-89791-362-1
T2 - Proceedings of the 6th annual symposium on Computational geometry
TI - Euclidean minimum spanning trees and bichromatic closest pairs
ER -