Average Case Analysis of Leaf-Centric Binary Tree Sources

Authors Louisa Seelbach Benkner, Markus Lohrey

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Louisa Seelbach Benkner
  • Universität Siegen, Germany
Markus Lohrey
  • Universität Siegen, Germany

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Louisa Seelbach Benkner and Markus Lohrey. Average Case Analysis of Leaf-Centric Binary Tree Sources. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 16:1-16:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We study the average size of the minimal directed acyclic graph (DAG) with respect to so-called leaf-centric binary tree sources as studied by Zhang, Yang, and Kieffer. A leaf-centric binary tree source induces for every n >= 2 a probability distribution on all binary trees with n leaves. We generalize a result shown by Flajolet, Gourdon, Martinez and Devroye according to which the average size of the minimal DAG of a binary tree that is produced by the binary search tree model is Theta(n / log n).

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Enumeration
  • Directed acylic graphs
  • average case analysis
  • tree compression


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