Exact-Size Sampling of Enriched Trees in Linear Time
Abstract.
We create a novel connection between Boltzmann sampling methods and Devroye’s algorithm to develop highly efficient sampling procedures that generate objects from important combinatorial classes with a given size \(n\) in expected time \(O(n)\) . This performance is best possible and significantly improves the state of the art for samplers of subcritical graph classes (such as cactus graphs, outerplanar graphs, and series-parallel graphs), subcritical substitution-closed classes of permutations, Bienaymé–Galton–Watson trees conditioned on their number of leaves, and several further examples. Our approach allows for this high level of universality, as it applies in general to classes admitting bijective encodings by so-called enriched trees, which are rooted trees with additional structures on the offspring of each node.
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Acknowledgment.
We thank the referees for the thorough reading of the manuscript and the helpful comments.
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© 2023 Society for Industrial and Applied Mathematics.
History
Submitted: 17 November 2021
Accepted: 26 June 2023
Published online: 4 October 2023
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Deutsche Forschungsgemeinschaft (DFG): PA 2080/3-1
European Research Council (ERC): 772606-PTRCSP
Funding: The first author’s research was supported by the European Research Council, ERC Grant Agreement 772606-PTRCSP. The second author’s research was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Project PA 2080/3-1.
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