On the silhouette of binary search trees

Rudolf Grübel

doi:10.1214/08-AAP593

On the silhouette of binary search trees

Probability 2009-10-21 v1

Authors: Rudolf Grübel

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Abstract

A zero-one sequence describes a path through a rooted directed binary tree $T$ ; it also encodes a real number in $[0,1]$ . We regard the level of the external node of $T$ along the path as a function on the unit interval, the silhouette of $T$ . We investigate the asymptotic behavior of the resulting stochastic processes for sequences of trees that are generated by the binary search tree algorithm.

Keywords

binary search tree silhouette stochastic process asymptotic behavior random tree path encoding

Cite

@article{arxiv.0910.3825,
  title  = {On the silhouette of binary search trees},
  author = {Rudolf Grübel},
  journal= {arXiv preprint arXiv:0910.3825},
  year   = {2009}
}

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Published in at http://dx.doi.org/10.1214/08-AAP593 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

On the silhouette of binary search trees

Abstract

Keywords

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