On the distribution of binary search trees under the random permutation model

• Published in: Random structures & algorithms Vol. 8; no. 1; pp. 1 - 25
• Main Author: Fill, James Allen
• Format: Journal Article
• Language: English
• Published: New York Wiley Subscription Services, Inc., A Wiley Company 01-01-1996
• ISSN: 1042-9832; 1098-2418
• DOI: 10.1002/(SICI)1098-2418(199601)8:1<1::AID-RSA1>3.0.CO;2-1

We study the distribution Q on the set Bn of binary search trees over a linearly ordered set of n records under the standard random permutation model. This distribution also arises as the stationary distribution for the move‐to‐root (MTR) Markov chain taking values in Bn when successive requests are independent and identically distributed with each record equally likely. We identify the minimum and maximum values of the functional Q and the trees achieving those values and argue that Q is a crude measure of the “shape” of the tree. We study the distribution of Q(T) for two choices of distribution for random trees T; uniform over Bn and Q. In the latter case, we obtain a limiting normal distribution for −ln Q(T). © 1996 John Wiley & Sons, Inc.