## Abstract

A parameterized binary search tree called iR tree is defined in this paper. A user is allowed to select a level of balance he desires. SR tree is a special case of iR tree when i=1. There are two new concepts in SR trees: (1) local balancing scheme that balances the tree locally; (2) consecutive storage for brother nodes that reduces pointer space. Although we may introduce empty nodes into the tree, we can show that only 1/8 of the nodes may be empty on the average, so it may still be advantageous in cases when record sizes are small. Insertion (and deletion) into SR trees can be done in time h + O(1) where h is the height of the tree. The average searching time for SR trees is shown to be 1.188 log<inf>2</inf>k where k is the number of keys. Generalization of the results of SR trees to iR in general is also given. © 1983 BIT Foundations.