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Optimal Antimatroid Sorting

Author Benjamin Aram Berendsohn

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  • Theory of computation → Design and analysis of algorithms
Keywords
  • sorting
  • working-set heap
  • greedy
  • antimatroid

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Abstract

The classical comparison-based sorting problem asks us to find the underlying total ordering 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 orderings is given, usually in some compressed form.
Recently, an algorithm called topological heapsort with optimal running time was found for 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 partial ordering [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.

Cite As Get BibTex

Benjamin Aram Berendsohn. Optimal Antimatroid Sorting. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 104:1-104:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ESA.2025.104

Author Details

Benjamin Aram Berendsohn
  • Max Planck Institute for Informatics, Saarbrücken, Germany

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