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 log 2 n+n log 2 m) in E 3 , which yields an O(N 4/3 log 4/3 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) 1-1/([d/2]+1)+ε +m log n+n log m) for the bichromatic closest pair problem and O(N 2-2/([d/2]+1)ε ) for the Euclidean minimum spanning tree problem, for any positive e{open}. © 1991 Springer-Verlag New York Inc.