Summary
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 H n/(c log(n)) tends to 1 in probability and in the mean as n→∞, where H n 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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Research of the author was sponsored by NSERC Grant A3456 and by FCAC Grant EQ-1678
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Devroye, L. Branching processes in the analysis of the heights of trees. Acta Informatica 24, 277–298 (1987). https://doi.org/10.1007/BF00265991
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DOI: https://doi.org/10.1007/BF00265991