On the Analysis of the Average Height of a Digital Trie: Another Approach

The average height of a digital me has been recently investigated in many papers [2]-[8]. In most works on binary digital tries, a Bernoulli model and independent keys are assumed. We relax these assumptions in that V-ary asymmetric tries. Bernoulli and Poisson models. and dependent keys are considered. We show that the average height of the trie is asymptotically equal to 2 19u n (for the Bernoulli model) and 2 19w J.L (the Poisson model) where n and I.l are the number of records and the v average number of records respectively. The parameter u is defined as u-1 = L p? i=l and the V elements of the alphabet are dislributed according to probabilities Pi. i = 1 I ••• , V. Finally, a generalization to the so called b -tries is discussed. In contrast to the previous analysis. our approach is very simple since we avoid explicit computation of lhe height disttibutioIL "' and the Technical UniversiLy of Gdansk., Poiwld