A Markov chain model for dynamic binary search tree behaviour

Abstract

We present a Markov chain model for the analysis of the behaviour of binary search trees (BSTs) under the dynamic conditions of insertions and deletions. The model is based on a data structure called a lineage tree, which provides a compact representation of different BST structures while still retaining enough information to model the effect of insertions and deletions and to compute average path length and tree height. Different lineages in the lineage tree correspond to states in the Markov chain. Transition probabilities are based on the number of BST structures corresponding to each lineage. The model is based on a similar lineage tree model developed for B-trees. The BST model is not intended for practical computations, but rather as a demonstration of the generalizability of the lineage tree approach for modeling data structures such as B-trees, B*-trees, B⁺-trees, BSTs, etc.

Keywords:

• Binary search tree
• B-tree
• Markov chain