The expected profile of digital search trees
Journal of Combinatorial Theory Series A
Renewal theory in the analysis of tries and strings
Theoretical Computer Science
| Hi-index | 754.84 |
A complete characterization of a digital tree, also called a trie, is presented from the depth viewpoint in a Markovian framework, that is, under the assumption that symbols in a key are Markov-dependent. The main findings show that asymptotically, as the number of keys n tends to infinity, the average depth becomes EDn~(1/ h1) log N+c', and the variance is var Dn~α log n+c", where h1 is the entropy of the (Markovian-dependent) alphabet, α is a parameter of the probabilistic model and c ' and c" are constants. The symmetric independent model has α=0, hence in this case var Dn=O(1). Limiting distribution is also derived for the depth Dn, and in particular, it is shown that Dn tends to the normal distribution in all cases except the symmetric independent model. These results extend all previous analyses since most of them have been limited to independent models