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DOI: 10.4230/LIPIcs.AofA.2024.2

Enumeration and Succinct Encoding of AVL Trees

Authors: Jeremy Chizewer, Stephen Melczer, J. Ian Munro, and Ava Pun

Published in: LIPIcs, Volume 302, 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)

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)

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@InProceedings{chizewer_et_al:LIPIcs.AofA.2024.2,
  author =	{Chizewer, Jeremy and Melczer, Stephen and Munro, J. Ian and Pun, Ava},
  title =	{{Enumeration and Succinct Encoding of AVL Trees}},
  booktitle =	{35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)},
  pages =	{2:1--2:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-329-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{302},
  editor =	{Mailler, C\'{e}cile and Wild, Sebastian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2024.2},
  URN =		{urn:nbn:de:0030-drops-204376},
  doi =		{10.4230/LIPIcs.AofA.2024.2},
  annote =	{Keywords: AVL trees, analytic combinatorics, succinct data structures, enumeration}
}

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Enumeration and Succinct Encoding of AVL Trees

Abstract

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