On the correspondence between AVL trees and brother trees

Abstract

We discuss the relationships of the classes of height-balanced (search) trees and the classes of brother (search) trees. In particular we characterize each class of height-balanced trees in terms of the class of “corresponding” brother trees and vice versa. Secondly, we show how this characterization leads to the notion of nonstandard updating algorithms. We derive a nonstandard insertion algorithm for height-balanced search trees to illustrate the notion. Finally we consider something of the similarities and differences between the standard and nonstandard insertion algorithms for height-balanced search rees.