On the Horton-Strahler Number for Combinatorial Tries

On the Horton-Strahler Number for Random Tries

We consider random tries constructedfrom n i.i.d. séquences of independent Bernoulli (p) random variables, 0 < p < 1. We study the Horton-Strahler number Hn, and show that ëmin(p,l-p) in probability as n —*• oo.

A Note on the Horton-Strahler Number for Random Trees

We consider the Horton-Strahler number S, for random equiprobable binary trees with n nodes. We give a simple probabilistic proof of the well-known result that ES, = log,n + O(1) and show that for every x > 0, P{ 1 S, log,n ( > x} Q D/4x, for some constant D > 0.

The Stack-Size of Combinatorial Tries Revisited

In the present paper we consider a generalized class of extended binary trees in which leaves are distinguished in order to represent the location of a key within a trie of the same structure. We prove an exact asymptotic equivalent to the average stack-size of trees with α internal nodes and β leaves corresponding to keys; we assume that all trees with the same parameters α and β have the same...

The Sta k - Size of Combinatorial Tries

On the number of full levels in tries

We study the asymptotic distribution of the ll-up level in a binary trie built over n independent strings generated by a biased memoryless source. The ll-up level is the number of full levels in a tree. A level is full if it contains the maximum allowable number of nodes (e.g., in a binary tree level k can have up to 2 nodes). The ll-up level nds many interesting applications, e.g., in the inte...