Limit Laws for Sums of Functions of Subtrees of Random Binary Search Trees

We consider sums of functions of subtrees of a random binary search tree, and obtain general laws of large numbers and central limit theorems. These sums correspond to random recurrences of the quicksort type, Xn L = XIn +Xn-1-In +Yn, n 1, where In is uniformly distributed on {0, 1, . . . , n - 1}, Yn is a given random variable, Xk L = Xk for all k, and given In, XIn and Xn-1-In are independent. Conditions are derived such that (Xn -

• Type: Journal
• Year: 2002
• Where: SIAMCOMP
• Authors: Luc Devroye
• Keywords: Binary Search Tree, Random, Random Binary Search, SIAMCOMP 2002