Protected node profile of Tries

Mehri Javanian (1)

1 University of Zanjan, Zanjan

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.

Mots clés: Mellin transform; Generating func- tions; Generating func tions; Poissonization; tries; protected nodes; tree profiles; recurrences; generating functions; singularity analysis; saddle point method

Domaines: Mathématiques [math]; Combinatoire [math.CO]

Mehri Javanian. Protected node profile of Tries. Discrete Mathematics and Theoretical Computer Science, 2018, Vol. 20 no. 1, ⟨10.23638/DMTCS-20-1-12⟩. ⟨hal-01548175v6⟩