On the joint distribution of the nodes in uniform multidimensional binary trees

Abstract

Multidimensional binary trees represent a symbiosis of trees and tries, and they essentially arise in the construction of search trees for multidimensional keys. The set of nodes in a d-dimensional binary tree can be partitioned into layers according to the nodes appearing in the ith dimension. We determine the exact distribution of the number of nodes with zero, one, and two sons in a specified layer and show that jointly the three types of nodes asymptotically have a trivariate normal distribution in each layer. That trivariate normal distribution is completely characterized. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 13: 261–283, 1998