Succinct Encodings of Binary Trees with Application to AVL Trees
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912560517742592 |
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| author | Chizewer, Jeremy Melczer, Stephen Munro, J. Ian Pun, Ava |
| author_facet | Chizewer, Jeremy Melczer, Stephen Munro, J. Ian Pun, Ava |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_15511 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Succinct Encodings of Binary Trees with Application to AVL Trees Chizewer, Jeremy Melczer, Stephen Munro, J. Ian Pun, Ava Combinatorics Data Structures and Algorithms 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. |
| title | Succinct Encodings of Binary Trees with Application to AVL Trees |
| topic | Combinatorics Data Structures and Algorithms |
| url | https://arxiv.org/abs/2311.15511 |