LIPIcs.MFCS.2018.16.pdf
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Average Case Analysis of Leaf-Centric Binary Tree Sources
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43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Mathematical Foundations of Computer Science (MFCS) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2018-08-27
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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)
https://doi.org/10.4230/LIPIcs.MFCS.2018.16
Abstract
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
Keywords
- Directed acylic graphs
- average case analysis
- tree compression
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References
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