Numerical Studies of the Asymptotic Height Distribution in Binary Search Trees

We study numerically a non-linear integral equation that arises in the study of binary search trees. If the tree is constructed from n elements, this integral equation describes the asymptotic (as n → ∞) distribution of the height of the tree. The height is defined as the longest path in the tree. Our analysis supplements some asymptotic results we recently obtained (cf. Knessl and Szpankowski (2002)) for the tails of the distribution. The asymptotic height distribution is shown to be unimodal with highly asymmetric tails.