Explaining the behaviour of binary search trees under prolonged updates: a model and simulations

Abstract

We present an extensive study into the long-term behaviour of binary search trees subjected to updates using the usual deletion algorithms taught in introductory textbooks. We develop a model of the behaviour of such trees which leads us to conjecture that the asymptotic average search path length is Θ(N1/2). We present results of large simulations which strongly support this conjecture. However, introducing a simple modification to ensure symmetry in the algorithms, the model predicts no such long-term deterioration. Simulations in fact indicate that asymptotically the average path length of such trees is less than the 1.386...log2N average path length of trees generated from random insertion sequences.