Expected behaviour analysis of AVL trees

  • Ricardo Baeza-Yates
  • Gaston H. Gonnet
  • Nivio Ziviani
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 447)


In this paper we improve previous bounds on expected measures of AVL trees by using fringe analysis. A new way of handling larger tree collections that are not closed is presented. An inherent difficulty posed by the transformations necessary to keep the AVL tree balanced makes its analysis difficult when using fringe analysis methods. We derive a technique to cope with this difficulty obtaining the exact solution for fringe parameters even when unknown probabilities are involved. We show that the probability of a rotation in an insertion is between 0.37 and 0.73, that the fraction of balanced nodes is between 0.56 and 0.78, and that the expected number of comparisons in a search seems to be at most 12% more than in the complete balanced tree.


Expected Number Unknown Probability Random Insertion Tree Collection Fringe Analysis 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Ricardo Baeza-Yates
    • 1
  • Gaston H. Gonnet
    • 2
  • Nivio Ziviani
    • 3
  1. 1.Depto. de Cs. de la ComputaciónUniversidad de ChileSantiagoChile
  2. 2.Department of Computer ScienceUniversity of WaterlooWaterlooCanada
  3. 3.Depto. de Cíencia da ComputaçãoUniversidade Federal de Minas Gerais Belo HorizonteMinas GeraisBrazil

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