Bimodality and Phase Transitions in the Profile Variance of Random Binary Search Trees

@article{Drmota2005BimodalityAP,
  title={Bimodality and Phase Transitions in the Profile Variance of Random Binary Search Trees},
  author={Michael Drmota and Hsien-Kuei Hwang},
  journal={SIAM J. Discrete Math.},
  year={2005},
  volume={19},
  pages={19-45}
}
We show that the variance of the profiles (number of nodes at each level) of random binary search trees exhibits asymptotically four phase transitions and a bimodal or “two-hump ed” behavior, in contrast to the unimodality of the mean value of the profiles. Precise asymptotic appr oximations are derived. The same types of phenomena also hold for the profiles of random recursive trees. 

From This Paper

Figures, tables, and topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 36 references

Handbook of Mathematical Functions (with Formulas

  • M. Abramowitz, I. A. Stegun
  • Graphs a nd Mathematical Tables) , Dover, New…
  • 1965
Highly Influential
12 Excerpts

Probability distributions on cladograms

  • D. Aldous
  • Random Discrete Structures , Edited by D. Aldous…
  • 1996
Highly Influential
8 Excerpts

A survey of recursive tree s,Theory of Probabability and Mathematical Statistics

  • R. T. Smythe, H. M. Mahmoud
  • 1995
Highly Influential
4 Excerpts

On growing random binary trees

  • B. G. Pittel
  • Journal of Mathematical Analysis and Applications…
  • 1984
Highly Influential
5 Excerpts

Mar tingales

  • B. Chauvin, T. Klein, J.-F. Marckert, A. Rouault
  • embedding and tilting of binary trees, preprint
  • 2003
Highly Influential
5 Excerpts

Similar Papers

Loading similar papers…