Nicolas Broutin ; Philippe Flajolet - The height of random binary unlabelled trees

dmtcs:3559 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science - https://doi.org/10.46298/dmtcs.3559
The height of random binary unlabelled trees

Authors: Nicolas Broutin 1; Philippe Flajolet 1

  • 1 Algorithms

This extended abstract is dedicated to the analysis of the height of non-plane unlabelled rooted binary trees. The height of such a tree chosen uniformly among those of size $n$ is proved to have a limiting theta distribution, both in a central and local sense. Moderate as well as large deviations estimates are also derived. The proofs rely on the analysis (in the complex plane) of generating functions associated with trees of bounded height.

https://doi.org/10.46298/dmtcs.3559
Source: HAL:hal-01194678v1
Volume: DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science
Section: Proceedings
Published on: January 1, 2008
Imported on: May 10, 2017
Keywords: Average case analysis,height,limit distribution,local limit theorem,generating functions,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

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Source : ScholeXplorer IsRelatedTo DOI 10.1017/s0963548300000560
  • 10.1017/s0963548300000560
  • 10.1017/s0963548300000560
The Distribution of heights of binary trees and other simple trees

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