RAIRO-Theor. Inf. Appl.
Volume 56, 2022
|Number of page(s)||8|
|Published online||07 February 2022|
Weakly protected nodes in random binary search trees
Department of Statistics, Faculty of Mathematical Sciences, University of Tabriz,
2 Department of Statistics, Faculty of Sciences, University of Zanjan, Zanjan, Iran.
* Corresponding author: firstname.lastname@example.org
Accepted: 17 January 2022
Here, we derive the exact mean and variance of the number of weakly protected nodes (the nodes that are not leaves and at least one of their children is not a leaf) in binary search trees grown from random permutations. Furthermore, by using contraction method, we prove normal limit law for a properly normalized version of this tree parameter.
Mathematics Subject Classification: 05C05 / 05C80 / 60F05
Key words: Random binary search tree / Weakly protected nodes / Zolotarev metric / Contraction method / limiting distribution
© The authors. Published by EDP Sciences, 2022
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