Varieties of Increasing Trees

We extend results about heights of random trees (Devroye, 1986, 1987, 1998b). 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 (Bergeron et al., 1992). Keywords and phrases: Height, random tree, branching process, probabilistic analysis, increasing tree.

• Type: Conference
• Year: 1992
• Where: CAAP
• Authors: François Bergeron, Philippe Flajolet, Bruno Salvy
• Keywords: CAAP 1992, Normalized Subtree Sizes, Random Tree, Split Tree Model, Theoretical Computer Science