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 ACL tree). It is shown that deletion of an arbitrary node of such a tree can be accomplished in O(logn) 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. CACM June, 1978 Zweben, S. McDonald, M. Balanced, binary, search, trees 3.73 3.74 4.34 5.25 5.31 CA780601 DH February 26, 1979 12:48 PM 2839 4 3096 3009 4 3096 3042 4 3096 3042 4 3096 3065 4 3096 3096 4 3096 3096 4 3096 3096 4 3096 3163 4 3096 3163 4 3096 3163 4 3096 2839 5 3096 2889 5 3096 3009 5 3096 3065 5 3096 3096 5 3096 3096 5 3096 3096 5 3096 3163 5 3096 2839 6 3096 2839 6 3096 2889 6 3096 3009 6 3096 3065 6 3096 3096 6 3096 3096 6 3096