## The Annals of Applied Probability

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

### Normality of tree-growing search strategies

Russell Lyons and Kevin Zumbrun

#### Abstract

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

**Source**

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

**Dates**

First available in Project Euclid: 29 July 2002

**Permanent link to this document**

https://projecteuclid.org/euclid.aoap/1027961036

**Digital Object Identifier**

doi:10.1214/aoap/1027961036

**Mathematical Reviews number (MathSciNet)**

MR1620342

**Zentralblatt MATH identifier**

0941.68036

**Subjects**

Primary: 68P10: Searching and sorting

Secondary: 60F05: Central limit and other weak theorems

**Keywords**

Sort insert limit
distribution

#### Citation

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