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.
"Normality of tree-growing search strategies." Ann. Appl. Probab. 8 (1) 112 - 130, February 1998. https://doi.org/10.1214/aoap/1027961036