an:05303335
Zbl 1148.05024
Broutin, N.; Devroye, L.; McLeish, E.; de la Salle, M.
The height of increasing trees
EN
Random Struct. Algorithms 32, No. 4, 494-518 (2008).
00222355
2008
j
05C05 05C80
height; random tree; branching process; probabilistic analysis; increasing tree
Summary: We extend results about heights of random trees [\textit{L. Devroye}, J. Assoc. Comput. Mach. 33, No.\,3, 489--498 (1986; Zbl 0741.05062), SIAM J. Comp. 28, No.\,2, 409--432 (1998; Zbl 0915.68089)]. In this paper, a general split tree model is considered in which the normalized subtree sizes of nodes converge in distribution. The height of these trees is shown to be in probability asymptotic to \(c \log n\) for some constant \(c\). We apply our results to obtain a law of large numbers for the height of all polynomial varieties of increasing trees [\textit{F. Bergeron}, \textit{P. Flajolet} and \textit{B. Salvy}, Lect. Not. Comp. Sci. 581, 24--48 (1992)].
Zbl 0915.68089; Zbl 0741.05062