Multidimensional Balanced Binary Trees

A bstract-A new balanced multidimensional tree structure called a k-dimensional balanced binary tree, k a positive integer, is presented and investigated. It is shown that the data structure can be used to manage a set of n k-dimensional data items such that access, insertion, and deletion operations can be supported in Ooog n + k) time. The data structure is a multidimensional generalization of a balanced binary tree and retains much of the simplicity and efficiency of the base structure. The data structure requires O(k) single rotations for each insertion or deletion operation.