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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.06208 |
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| _version_ | 1866908515834003456 |
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| author | Ko, Jeremy |
| author_facet | Ko, Jeremy |
| contents | A binary trie is a sequential data structure for a dynamic set on the universe $\{0,\dots,u-1\}$ supporting Search with $O(1)$ worst-case step complexity, and Insert, Delete, and Predecessor operations with $O(\log u)$ worst-case step complexity.
We give a wait-free implementation of a relaxed binary trie, using read, write, CAS, and ($\log u$)-bit AND operations. It supports all operations with the same worst-case step complexity as the sequential binary trie. However, Predecessor operations may not return a key when there are concurrent update operations. We use this as a component of a lock-free, linearizable implementation of a binary trie. It supports Search with $O(1)$ worst-case step complexity and Insert, Delete and Predecessor with $O(c^2 + \log u)$ amortized step complexity, where $c$ is a measure of the contention.
A lock-free binary trie is challenging to implement as compared to many other lock-free data structures because Insert and Delete operations perform a non-constant number of modifications to the binary trie in the worst-case to ensure the correctness of Predecessor operations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06208 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Lock-free Binary Trie Ko, Jeremy Data Structures and Algorithms A binary trie is a sequential data structure for a dynamic set on the universe $\{0,\dots,u-1\}$ supporting Search with $O(1)$ worst-case step complexity, and Insert, Delete, and Predecessor operations with $O(\log u)$ worst-case step complexity. We give a wait-free implementation of a relaxed binary trie, using read, write, CAS, and ($\log u$)-bit AND operations. It supports all operations with the same worst-case step complexity as the sequential binary trie. However, Predecessor operations may not return a key when there are concurrent update operations. We use this as a component of a lock-free, linearizable implementation of a binary trie. It supports Search with $O(1)$ worst-case step complexity and Insert, Delete and Predecessor with $O(c^2 + \log u)$ amortized step complexity, where $c$ is a measure of the contention. A lock-free binary trie is challenging to implement as compared to many other lock-free data structures because Insert and Delete operations perform a non-constant number of modifications to the binary trie in the worst-case to ensure the correctness of Predecessor operations. |
| title | A Lock-free Binary Trie |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2405.06208 |