An Optimal Algorithm for Sorting Pattern-Avoiding Sequences
<|reference_start|>An Optimal Algorithm for Sorting Pattern-Avoiding Sequences: We present a deterministic comparison-based algorithm that sorts sequences avoiding a fixed permutation $\pi$ in linear time, even if $\pi$ is a priori unkown. Moreover, the dependence of the multiplicative constant on the pattern $\pi$ 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.<|reference_end|>
@article{opler2024an,
    title={An Optimal Algorithm for Sorting Pattern-Avoiding Sequences},
    author={Michal Opler},
    journal={arXiv preprint arXiv:2409.07868},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.07868},
    primaryClass={cs.DS}
}