On the subtree size profile of binary search trees

Authors:
Florian Dennert;Rudolf GrÜbel
Affiliations:
Institut für mathematische stochastik, leibniz universität hannover, postfach 6009, d-30060 hannover, germany (e-mail: dennert@stochastik.uni-hannover.de, rgrubel@stochastik.uni-hannover ...;Institut für mathematische stochastik, leibniz universität hannover, postfach 6009, d-30060 hannover, germany (e-mail: dennert@stochastik.uni-hannover.de, rgrubel@stochastik.uni-hannover ...
Venue:
Combinatorics, Probability and Computing
Year:
2010

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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.