Profile and Height of Random Binary Search Trees

The height of random binary unlabelled trees

This extended abstract is dedicated to the analysis of the height of non-plane unlabelled rooted binary trees. The height of such a tree chosen uniformly among those of size n is proved to have a limiting theta distribution, both in a central and local sense. Moderate as well as large deviations estimates are also derived. The proofs rely on the analysis (in the complex plane) of generating fun...

The Height of Binary Search Trees

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The Height of q-Binary Search Trees

The paper [8] introduces for the first time a meaningful q–model of binary search trees: instead of binary search trees, one considers tournament trees, which differ only marginally from binary search trees; if one starts from a permutation ( 1 2 ··· n π1 π2 ··· πn ) , then one inserts the number i instead of the number πi. Thus, traversing the tree in inorder, we might think of the associated ...

Martingales and Profile of Binary Search Trees

We are interested in the asymptotic analysis of the binary search tree (BST) under the random permutation model. Via an embedding in a continuous time model, we get new results, in particular the asymptotic behavior of the profile.

The Profile of Binary Search Trees