Galled Tree-Child Networks

Chang, Yu-Sheng; Fuchs, Michael; Yu, Guan-Ru

doi:10.4230/LIPIcs.AofA.2024.8

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Document Identifiers

DOI: 10.4230/LIPIcs.AofA.2024.8
URN: urn:nbn:de:0030-drops-204439

Author Details

Yu-Sheng Chang

Department of Mathematical Sciences, National Chengchi University, Taipei, Taiwan

Michael Fuchs

Department of Mathematical Sciences, National Chengchi University, Taipei, Taiwan

Guan-Ru Yu

Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan

Acknowledgements

We thank the three reviewers for positive feedback and useful suggestions. This paper is dedicated to Hsien-Kuei Hwang on the occasion of his 60th birthday.

Cite AsGet BibTex

Yu-Sheng Chang, Michael Fuchs, and Guan-Ru Yu. Galled Tree-Child Networks. In 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 8:1-8:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.AofA.2024.8

Abstract

We propose the class of galled tree-child networks which is obtained as intersection of the classes of galled networks and tree-child networks. For the latter two classes, (asymptotic) counting results and stochastic results have been proved with very different methods. We show that a counting result for the class of galled tree-child networks follows with similar tools as used for galled networks, however, the result has a similar pattern as the one for tree-child networks. In addition, we also consider the (suitably scaled) numbers of reticulation nodes of random galled tree-child networks and show that they are asymptotically normal distributed. This is in contrast to the limit laws of the corresponding quantities for galled networks and tree-child networks which have been both shown to be discrete.

Subject Classification

ACM Subject Classification

Mathematics of computing → Enumeration
Mathematics of computing → Distribution functions

Keywords

Phylogenetic Network
galled Network
tree-child Network
asymptotic Enumeration
Limit Law
Lagrange Inversion

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