LIPIcs.AofA.2022.5.pdf
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Enumeration of d-Combining Tree-Child Networks
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33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2022-06-08
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Yu-Sheng Chang, Michael Fuchs, Hexuan Liu, Michael Wallner, and Guan-Ru Yu. Enumeration of d-Combining Tree-Child Networks. In 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 225, pp. 5:1-5:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.AofA.2022.5
https://doi.org/10.4230/LIPIcs.AofA.2022.5
Abstract
Tree-child networks are one of the most prominent network classes for modeling evolutionary processes which contain reticulation events. Several recent studies have addressed counting questions for bicombining tree-child networks which are tree-child networks with every reticulation node having exactly two parents. In this paper, we extend these studies to d-combining tree-child networks where every reticulation node has now d ≥ 2 parents. Moreover, we also give results and conjectures on the distributional behavior of the number of reticulation nodes of a network which is drawn uniformly at random from the set of all tree-child networks with the same number of leaves.
Subject Classification
ACM Subject Classification
- Mathematics of computing → Discrete mathematics
Keywords
- Phylogenetic network
- tree-child network
- d-combining tree-child network
- exact enumeration
- asymptotic enumeration
- reticulation node
- limit law
- stretched exponential
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References
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