Abstract
It is shown how the theory of branching processes can be applied in the analysis of the expected height of random trees. In particular, we will study the height of random binary search trees, random k—d trees, quadtrees and union-find trees under various models of randomization. For example, for the random binary search tree constructed from a random permutation of 1,..., n, it is shown that Hn/(c log(n)) tends to 1 in probability and in the mean as n→∞, where Hn is the height of the tree, and c =4.31107... is a solution of the equation \(\left( {\frac{{2e}}{c}} \right) = 1\). In addition, we show that \(H_n - c log (n) = {\text{O}}(\sqrt {log(n)loglog(n)} )\) in probability.
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