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Enumeration of d-Combining Tree-Child Networks

Authors Yu-Sheng Chang, Michael Fuchs, Hexuan Liu, Michael Wallner, Guan-Ru Yu

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Author Details

Yu-Sheng Chang
  • Department of Mathematical Sciences, National Chengchi University, Taipei, 116, Taiwan
Michael Fuchs
  • Department of Mathematical Sciences, National Chengchi University, Taipei, 116, Taiwan
Hexuan Liu
  • Department of Mathematical Sciences, National Chengchi University, Taipei, 116, Taiwan
Michael Wallner
  • Institute of Discrete Mathematics and Geometry, TU Wien, Vienna, 1040, Austria
Guan-Ru Yu
  • Department of Mathematics, National Kaohsiung Normal University, Kaohsiung, 824, Taiwan

Funding

  • Fuchs, Michael: Partially supported by MOST-109-2115-M-004-003-MY2.
  • Wallner, Michael: Supported by the Austrian Science Fund (FWF): P 34142.
  • Yu, Guan-Ru: Partially supported by MOST-110-2115-M-017-003-MY3.

Cite As Get BibTex

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

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

  1. Gabriel Cardona and Louxin Zhang. Counting and enumerating tree-child networks and their subclasses. J. Comput. System Sci., 114:84-104, 2020. Google Scholar
  2. Yu-Sheng Chang, Michael Fuchs, Hexuan Liu, Michael Wallner, and Guan-Ru Yu. Maple worksheet, 2021. URL: http://arxiv.org/abs/2203.07619.
  3. Andrew Elvey Price, Wenjie Fang, and Michael Wallner. Asymptotics of minimal deterministic finite automata recognizing a finite binary language. In 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, volume 159:Art. No. 11, 13 pages of LIPIcs. Leibniz Int. Proc. Inform. Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, 2020. Google Scholar
  4. Andrew Elvey Price, Wenjie Fang, and Michael Wallner. Compacted binary trees admit a stretched exponential. J. Combin. Theory Ser. A, 177:Paper No. 105306, 40 pages, 2021. Google Scholar
  5. Michael Fuchs, Bernhard Gittenberger, and Marefatollah Mansouri. Counting phylogenetic networks with few reticulation vertices: tree-child and normal networks. Australas. J. Combin., 73:385-423, 2019. Google Scholar
  6. Michael Fuchs, Bernhard Gittenberger, and Marefatollah Mansouri. Counting phylogenetic networks with few reticulation vertices: exact enumeration and corrections. Australas. J. Combin., 81:257-282, 2021. Google Scholar
  7. Michael Fuchs, En-Yu Huang, and Guan-Ru Yu. Counting phylogenetic networks with few reticulation vertices: a second approach. URL: http://arxiv.org/abs/2104.07842.
  8. Michael Fuchs, Hexuan Liu, and Guan-Ru Yu. A short note on the exact counting of tree-child networks. arXiv:2110.03842. URL: http://arxiv.org/abs/2110.03842.
  9. Michael Fuchs, Guan-Ru Yu, and Louxin Zhang. On the asymptotic growth of the number of tree-child networks. European J. Combin., 93:Paper No. 103278, 2021. Google Scholar
  10. Daniel H. Huson, Regula Rupp, and Celine Scornavacca. Phylogenetic Networks: Concepts, Algorithms and Applications. Cambridge University Press, 1st edition, 2010. Google Scholar
  11. Colin McDiarmid, Charles Semple, and Dominic Welsh. Counting phylogenetic networks. Ann. Comb., 19(1):205-224, 2015. Google Scholar
  12. Miquel Pons and Josep Batle. Combinatorial characterization of a certain class of words and a conjectured connection with general subclasses of phylogenetic tree-child networks. Sci. Rep., 11:Article number: 21875, 2021. Google Scholar
  13. Mike Steel. Phylogeny - discrete and random processes in evolution, volume 89 of CBMS-NSF Regional Conference Series in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2016. Google Scholar
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