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Communications of the ACM

An optimal method for deletion in one-sided height-balanced trees


A one-sided height-balanced tree is a binary tree in which every node's right subtree has a height which is equal to or exactly one greater than the height of its left subtree. It has an advantage over the more general AVL tree in that only one bit of balancing information is required (two bits are required for the AVL tree). It is shown that deletion of an arbitrary node of such a tree can be accomplished in O(log n) operations, where n is the number of nodes in the tree. Moreover the method is optimal in the sense that its complexity cannot be reduced in order of magnitude. This result, coupled with earlier results by Hirschberg, indicates that, of the three basic problems of insertion, deletion, and retrieval, only insertion is adversely affected by this modification of an AVL tree.

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