| Issue |
RAIRO-Theor. Inf. Appl.
Volume 34, Number 4, July/August 2000
|
|
|---|---|---|
| Page(s) | 279 - 296 | |
| DOI | https://doi.org/10.1051/ita:2000117 | |
| Published online | 15 April 2002 | |
On the Horton-Strahler Number for Combinatorial Tries
Johann Wolfgang Goethe-Universität,
Fachbereich Informatik, Senckenbergenlage 31, 60054 Frankfurt am
Main, Germany.
Received:
15
February
2000
Accepted:
3
October
2000
In this paper we investigate the average Horton-Strahler number of all possible tree-structures of binary tries. For
that purpose we consider a generalization of extended binary trees where leaves are distinguished in order to represent
the location of keys within a corresponding trie. Assuming a uniform distribution for those trees we prove that the
expected Horton-Strahler number of a tree with α internal nodes and β leaves that correspond to a key is
asymptotically given by 
provided that α and β
grow in some fixed proportion ρ when α → ∞ . A similar result is shown for trees with α
internal nodes but with an arbitrary number of keys.
Mathematics Subject Classification: 05A15 / 05C05 / 68W40
© EDP Sciences, 2000
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