On the Subtree Size Profile of Binary Search trees

Source abstract

For random trees T generated by the binary search tree algorithm from uniformly distributed input we consider the subtree size profile, which maps k ∈ ℕ to the number of nodes in T that root a subtree of size k . Complementing earlier work by Devroye, by Feng, Mahmoud and Panholzer, and by Fuchs, we obtain results for the range of small k -values and the range of k -values proportional to the size n of T . In both cases emphasis is on the process view, i.e. , the joint distributions for several k -values. We also show that the dynamics of the tree sequence lead to a qualitative difference between the asymptotic behaviour of the lower and the upper end of the profile.