In a rooted tree, protected nodes are neither leaves nor parents of any leaves. They have some practical motivations, e.g., in organizational schemes, security models and social-network models. Protected node profile measures the number of protected nodes with the same distance from the root in rooted trees. For no rooted tree, protected node profile has been investigated so far. Here, we present the asymptotic expectations, variances, covariance and limiting bivariate distribution of protected node profile and non-protected internal node profile in random tries, an important data structure on words in computer science. Also we investigate the fraction of these expectations asymptotically. These results are derived by the methods of analytic combinatorics such as generating functions, Mellin transform, Poissonization and depoissonization, saddle point method and singularity analysis.

Source : oai:HAL:hal-01710494v6

DOI : 10.23638/DMTCS-20-1-12

Volume: Vol. 20 no. 1

Section: Analysis of Algorithms

Published on: March 26, 2018

Submitted on: June 27, 2017

Keywords: Mellin transform,Generating func- tions,Generating func tions,Poissonization,tries,protected nodes,tree profiles,recurrences,generating functions,singularity analysis,saddle point method,
[
MATH
]
Mathematics [math],
[
MATH.MATH-CO
]
Mathematics [math]/Combinatorics [math.CO]

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