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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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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Enumeration
Keywords
  • AVL trees
  • analytic combinatorics
  • succinct data structures
  • enumeration

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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.

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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

Author Details

Jeremy Chizewer
  • University of Waterloo, Canada
Stephen Melczer
  • University of Waterloo, Canada
J. Ian Munro
  • University of Waterloo, Canada
Ava Pun
  • University of Waterloo, Canada

Funding

  • Melczer, Stephen: SM and JC partially funded by NSERC Discovery Grant RGPIN-2021-02382.
  • Munro, J. Ian: JIM and AP partially funded by NSERC Discovery Grant RGPIN-2018-03972.

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.

References

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