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Colloquium on Trees in Algebra and Programming

CAAP 1992: CAAP '92 pp 24–48Cite as

Varieties of increasing trees

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 581))

Abstract

An increasing tree is a labelled rooted tree in which labels along any branch from the root go in increasing order. Under various guises, such trees have surfaced as tree representations of permutations, as data structures in computer science, and as probabilistic models in diverse applications.

We present a unified generating function approach to the enumeration of parameters on such trees. The counting generating functions for several basic parameters are shown to be related to a simple ordinary differential equation, d/dzY(z)=φ(Y(z)), which is non linear and autonomous.

Singularity analysis applied to the intervening generating functions then permits to analyze asymptotically a number of parameters of the trees, like: root degree, number of leaves, path length, and level of nodes. In this way it is found that various models share common features: path length is O(n log n), the distribution of node levels and number of leaves are asymptotically normal, etc.

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Author information

Authors and Affiliations

  1. LACIM Université du Québec à Montréal, Succursale A, Case Postale 8888, H3C3P8, Montréal, Québec, Canada

    François Bergeron

  2. Algorithms Project INRIA Rocquencourt, 78153, Le Chesnay, France

    Philippe Flajolet & Bruno Salvy

Authors
  1. François Bergeron
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  2. Philippe Flajolet
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  3. Bruno Salvy
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Editor information

J. -C. Raoult

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© 1992 Springer-Verlag Berlin Heidelberg

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Bergeron, F., Flajolet, P., Salvy, B. (1992). Varieties of increasing trees. In: Raoult, J.C. (eds) CAAP '92. CAAP 1992. Lecture Notes in Computer Science, vol 581. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55251-0_2

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  • DOI: https://doi.org/10.1007/3-540-55251-0_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55251-2

  • Online ISBN: 978-3-540-46799-1

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