| Issue |
RAIRO-Theor. Inf. Appl.
Volume 56, 2022
|
|
|---|---|---|
| Article Number | 2 | |
| Number of page(s) | 8 | |
| DOI | https://doi.org/10.1051/ita/2022002 | |
| Published online | 07 February 2022 | |
Weakly protected nodes in random binary search trees
1
Department of Statistics, Faculty of Mathematical Sciences, University of Tabriz,
Tabriz Iran.
2
Department of Statistics, Faculty of Sciences, University of Zanjan,
Zanjan, Iran.
* Corresponding author: javanian@znu.ac.ir
Received:
23
May
2021
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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