Multidimensional Height-Balanced Trees

A new multidimensional balanced tree structure is presented for the efficient management of multidimensional data. It is shown that the data structure can be used to manage a set of n k-dimensional records or data items such that the records can be searched or updated in O(log2 n) + k time, which is optimal. The data structure is a multidimensional generalization of the height-balanced trees and retains much of their simplicity and efficiency. The insertion algorithm, in particular, retains a very important property of the height-balanced trees: an insertion of a record results in the application of a restructuring operation at most once.