On the Horton-Strahler number for random tries

On the Horton-Strahler Number for Combinatorial Tries

“…Thus it becomes possible to express the average Horton-Strahler number of (a,/3)-tries on dependence of a only. We conclude this discussion by noting that lim a-KX) 4«+!a* \a-l) 2…”

“…The Horton-Strahler number of tries has been investigated in a recent work by Devroye and Kruszewski [4]. A trie is a binary tree which is used to store the set of keys K = {&i,.…”

A unified approach to the analysis of Horton‐Strahler parameters of binary tree structures

“…ϭ :͑͒ holds. We will first consider the series () appearing in (6). The analysis of harmonic summations like () is performed by means of the Mellin transform which by now is a fairly well-understood methodology in analytic combinatorics and analysis of algorithms (see, for instance, the excellent survey by Flajolet, Gourdon, and Dumas [14]) going back to the seminal paper of De Bruijn, Knuth, and Rice [4].…”

“…Here, a node is called critical if its two subtrees possess the same value of hs, i.e., if it is responsible for a growth of the Horton-Strahler number. Recently, the author determined the average Horton-Strahler number of a class of trees (called Ꮿ-tries), which model the trie data structure in a combinatorial way [26]; the Horton-Strahler number of tries in the Bernoulli model has been investigated in [6]. The combinatorics of the Horton-Strahler analysis has been used in computer graphics for the creation of faithful synthetic images of natural trees (see [34]) and for information visualization [16].…”

The register function for t -ary trees

“…The concept has been extended to unary-binary trees [5]. Various papers about the register function (or Horton-Strahler numbers) have been written; we cite a few here [2,9,15,13,11].…”