LIPIcs.AofA.2024.2.pdf
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Enumeration and Succinct Encoding of AVL Trees
Authors
Jeremy Chizewer 
,
Stephen Melczer ,
J. Ian Munro ,
Ava Pun
-
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35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-07-18
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Acknowledgements
The authors thank Andrew Odlyzko for discussions on the asymptotic behaviour of AVL trees and the growth constant α, and thank Sebastian Wild for alerting us to relevant references.
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Jeremy Chizewer, Stephen Melczer, J. Ian Munro, and Ava Pun. Enumeration and Succinct Encoding of AVL Trees. In 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 2:1-2:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.AofA.2024.2
Abstract
We use a novel decomposition to create succinct data structures - supporting a wide range of operations on static trees in constant time - for a variety of tree classes, extending results of Munro, Nicholson, Benkner, and Wild. Motivated by the class of AVL trees, we further derive asymptotics for the information-theoretic lower bound on the number of bits needed to store tree classes whose generating functions satisfy certain functional equations. In particular, we prove that AVL trees require approximately 0.938 bits per node to encode.
Subject Classification
ACM Subject Classification
- Mathematics of computing → Enumeration
Keywords
- AVL trees
- analytic combinatorics
- succinct data structures
- enumeration
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References
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