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Almost sure asymptotics for the random binary search tree

Abstract : We consider a (random permutation model) binary search tree with $n$ nodes and give asymptotics on the $\log$ $\log$ scale for the height $H_n$ and saturation level $h_n$ of the tree as $n \to \infty$, both almost surely and in probability. We then consider the number $F_n$ of particles at level $H_n$ at time $n$, and show that $F_n$ is unbounded almost surely.
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  • HAL Id : hal-00459166, version 1

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Matthew Roberts. Almost sure asymptotics for the random binary search tree. 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), 2010, Vienna, Austria. pp.565-576. ⟨hal-00459166⟩

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