The Annals of Applied Probability

Normality of tree-growing search strategies

Russell Lyons and Kevin Zumbrun

Full-text: Open access


We study the class of tree-growing search strategies introduced by Lent and Mahmoud, searches for which data are stored in a deterministic sequence of tree structures (e.g., linear search in forward order). Specifically, we study the conditions under which the number of comparisons needed to sort a sequence of randomly ordered numbers is asymptotically normal. Our main result is a sufficient condition for normality in terms of the growth rate of tree height alone; this condition is easily computed and is satisfied by all standard deterministic search strategies. We also give some examples of normal search strategies with surprisingly small variance, in particular, much smaller than is possible for the class of consistent strategies that are the focus of the work by Lent and Mahmoud.

Article information

Ann. Appl. Probab., Volume 8, Number 1 (1998), 112-130.

First available in Project Euclid: 29 July 2002

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 68P10: Searching and sorting
Secondary: 60F05: Central limit and other weak theorems

Sort insert limit distribution


Lyons, Russell; Zumbrun, Kevin. Normality of tree-growing search strategies. Ann. Appl. Probab. 8 (1998), no. 1, 112--130. doi:10.1214/aoap/1027961036.

Export citation


  • [1] Feller, W. (1971). An Introduction to Probability Theory and Its Applications 2, 2nd ed. Wiley, New York.
  • [2] Lent, J. H. and Mahmoud, H. M. (1996). On tree-growing search strategies. Ann. Appl. Probab. 6 1284-1302.
  • [3] Mahmoud, H. M. (1992). Evolution of Random Search Trees. Wiley, New York.