The Annals of Applied Probability

The Profile of Binary Search Trees

Brigitte Chauvin, Michael Drmota, and Jean Jabbour-Hattab

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We characterize the limiting behavior of the number of nodes in level $k$ of binary search trees $T_n$ in the central region $1.2 \log n \leq 2.8 \log n$. Especially we show that the width $\bar{V}_n$ (the maximal number of internal nodes at the same level) satisfies $\bar{V}_n \sim (n/\sqrt{4\pi\log n})$ as $n \to \infty$ a.s.

Article information

Ann. Appl. Probab., Volume 11, Number 4 (2001), 1042-1062.

First available in Project Euclid: 5 March 2002

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Zentralblatt MATH identifier

Primary: 60F17: Functional limit theorems; invariance principles 60Q25 05C05: Trees

Repartition of nodes for binary search trees martingales asymptotic series expansion complex analysis


Chauvin, Brigitte; Drmota, Michael; Jabbour-Hattab, Jean. The Profile of Binary Search Trees. Ann. Appl. Probab. 11 (2001), no. 4, 1042--1062. doi:10.1214/aoap/1015345394.

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