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2015 Asymptotic distribution of two-protected nodes in ternary search trees
Cecilia Holmgren, Svante Janson
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Electron. J. Probab. 20: 1-20 (2015). DOI: 10.1214/EJP.v20-3577


We study protected nodes in $m-$ary search trees, by putting them in context of generalized Pólya urns. We show that the number of two-protected nodes (the nodes that are neither leaves nor parents of leaves) in a random ternary search tree is asymptotically normal. The methods apply in principle to $m-$ary search trees with larger $m$ as well, although the size of the matrices used in the calculations grow rapidly with $m$; we conjecture that the method yields an asymptotically normal distribution for all $m \leq 26$.

The one-protected nodes, and their complement, i.e., the leaves, are easier to analyze. By using a simpler urn (that is similar to the one that has earlier been used to study the total number of nodes in $m-$ary search trees), we prove normal limit laws for the number of one-protected nodes and the number of leaves for all $m \leq 26$.


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Cecilia Holmgren. Svante Janson. "Asymptotic distribution of two-protected nodes in ternary search trees." Electron. J. Probab. 20 1 - 20, 2015.


Accepted: 5 February 2015; Published: 2015
First available in Project Euclid: 4 June 2016

zbMATH: 1327.60032
MathSciNet: MR3311222
Digital Object Identifier: 10.1214/EJP.v20-3577

Primary: 60C05
Secondary: 05C05, 60F05, 68P05


Vol.20 • 2015
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