Optimal antimatroid sorting
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911063928209408 |
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| author | Berendsohn, Benjamin Aram |
| author_facet | Berendsohn, Benjamin Aram |
| contents | The classical comparison-based sorting problem asks us to find the underlying total order of a given set of elements, where we can only access the elements via comparisons. In this paper, we study a restricted version, where, as a hint, a set $T$ of possible total orders is given, usually in some compressed form.
Recently, an algorithm called topological heapsort with optimal running time was found for the case where $T$ is the set of topological orderings of a given directed acyclic graph, or, equivalently, $T$ is the set of linear extensions of a given partial order [Haeupler et al. 2024]. We show that a simple generalization of topological heapsort is applicable to a much broader class of restricted sorting problems, where $T$ corresponds to a given antimatroid.
As a consequence, we obtain optimal algorithms for the following restricted sorting problems, where the allowed total orders are restricted by: a given set of monotone precedence formulas; the perfect elimination orders of a given chordal graph; or the possible vertex search orders of a given connected rooted graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13994 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal antimatroid sorting Berendsohn, Benjamin Aram Data Structures and Algorithms The classical comparison-based sorting problem asks us to find the underlying total order of a given set of elements, where we can only access the elements via comparisons. In this paper, we study a restricted version, where, as a hint, a set $T$ of possible total orders is given, usually in some compressed form. Recently, an algorithm called topological heapsort with optimal running time was found for the case where $T$ is the set of topological orderings of a given directed acyclic graph, or, equivalently, $T$ is the set of linear extensions of a given partial order [Haeupler et al. 2024]. We show that a simple generalization of topological heapsort is applicable to a much broader class of restricted sorting problems, where $T$ corresponds to a given antimatroid. As a consequence, we obtain optimal algorithms for the following restricted sorting problems, where the allowed total orders are restricted by: a given set of monotone precedence formulas; the perfect elimination orders of a given chordal graph; or the possible vertex search orders of a given connected rooted graph. |
| title | Optimal antimatroid sorting |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2507.13994 |