An Optimal Algorithm for Sorting Pattern-Avoiding Sequences
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909313246691328 |
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| author | Opler, Michal |
| author_facet | Opler, Michal |
| contents | We present a deterministic comparison-based algorithm that sorts sequences avoiding a fixed permutation $π$ in linear time, even if $π$ is a priori unkown. Moreover, the dependence of the multiplicative constant on the pattern $π$ matches the information-theoretic lower bound. A crucial ingredient is an algorithm for performing efficient multi-way merge based on the Marcus-Tardos theorem. As a direct corollary, we obtain a linear-time algorithm for sorting permutations of bounded twin-width. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07868 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Optimal Algorithm for Sorting Pattern-Avoiding Sequences Opler, Michal Data Structures and Algorithms We present a deterministic comparison-based algorithm that sorts sequences avoiding a fixed permutation $π$ in linear time, even if $π$ is a priori unkown. Moreover, the dependence of the multiplicative constant on the pattern $π$ matches the information-theoretic lower bound. A crucial ingredient is an algorithm for performing efficient multi-way merge based on the Marcus-Tardos theorem. As a direct corollary, we obtain a linear-time algorithm for sorting permutations of bounded twin-width. |
| title | An Optimal Algorithm for Sorting Pattern-Avoiding Sequences |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2409.07868 |