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arXiv · 2311.15511

Succinct Encodings of Binary Trees with Application to AVL Trees

Jeremy Chizewer·Stephen Melczer·J. Ian Munro·Ava Pun
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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 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, Ava Pun. 2023-11-27. Succinct Encodings of Binary Trees with Application to AVL Trees. https://arxiv.org/abs/2311.15511

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