3163	 An Optimal Insertion Algorithm for One-Sided Height-Balanced BInary Search Trees	 An algorithm for inserting an element into a one-sided height-balanced OSHB binary search tree is presented. The algorithm operates in time O log n where n is the number of nodes in the tree. This represents an improvement over the best previous ly known insertion algorithms of Hirschberg and Kosaraju which require time O log n . Moreover the O log n complexity is optimal. Earlier results have shown that deletion in such a structure can also be performed in O log n time. Thus the result of this paper gives a negative answer to the question of whether such trees should be the first examples of their kind where deletion has a smaller time complexity than insertion. Furthermore it can now be concluded that insertion deletion and retrieval in OSHB trees can be performed in the same time as the corresponding operations for the more general AVL trees to within a constant factor. However the insertion and deletion algorithms for OSHB trees appear much more complicated than the corresponding algorithms for AVL trees. Insertion one-sided height-balanced trees height-balanced trees binary trees search trees.
