# Euclidean minimum spanning trees and bichromatic closest pairs

Published

Journal Article

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.

### Duke Authors

### Cited Authors

- Agarwal, PK; Edelsbrunner, H; Schwarzkopf, O; Welzl, E

### Published Date

- January 1, 1990

### Start / End Page

- 203 - 210

### Citation Source

- Scopus