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arXiv · 2409.07868

An Optimal Algorithm for Sorting Pattern-Avoiding Sequences

Michal Opler
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Abstract

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.

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Michal Opler. 2024-09-12. An Optimal Algorithm for Sorting Pattern-Avoiding Sequences. https://arxiv.org/abs/2409.07868

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