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Documents authored by Yu, Guan-Ru

Document
DOI: 10.4230/LIPIcs.AofA.2024.8
Galled Tree-Child Networks

Authors: Yu-Sheng Chang, Michael Fuchs, and Guan-Ru Yu

Published in: LIPIcs, Volume 302, 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)

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.
Cite as

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)

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@InProceedings{chang_et_al:LIPIcs.AofA.2024.8,
  author =	{Chang, Yu-Sheng and Fuchs, Michael and Yu, Guan-Ru},
  title =	{{Galled Tree-Child Networks}},
  booktitle =	{35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)},
  pages =	{8:1--8:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-329-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{302},
  editor =	{Mailler, C\'{e}cile and Wild, Sebastian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2024.8},
  URN =		{urn:nbn:de:0030-drops-204439},
  doi =		{10.4230/LIPIcs.AofA.2024.8},
  annote =	{Keywords: Phylogenetic Network, galled Network, tree-child Network, asymptotic Enumeration, Limit Law, Lagrange Inversion}
}
Document
DOI: 10.4230/LIPIcs.AofA.2022.5
Enumeration of d-Combining Tree-Child Networks

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

Published in: LIPIcs, Volume 225, 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022)

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.
Cite as

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)

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@InProceedings{chang_et_al:LIPIcs.AofA.2022.5,
  author =	{Chang, Yu-Sheng and Fuchs, Michael and Liu, Hexuan and Wallner, Michael and Yu, Guan-Ru},
  title =	{{Enumeration of d-Combining Tree-Child Networks}},
  booktitle =	{33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022)},
  pages =	{5:1--5:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-230-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{225},
  editor =	{Ward, Mark Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2022.5},
  URN =		{urn:nbn:de:0030-drops-160914},
  doi =		{10.4230/LIPIcs.AofA.2022.5},
  annote =	{Keywords: Phylogenetic network, tree-child network, d-combining tree-child network, exact enumeration, asymptotic enumeration, reticulation node, limit law, stretched exponential}
}
Document
DOI: 10.4230/LIPIcs.AofA.2018.19
The Number of Double Triangles in Random Planar Maps

Authors: Michael Drmota and Guan-Ru Yu

Published in: LIPIcs, Volume 110, 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)

Abstract
The purpose of this paper is to provide a central limit theorem for the number of occurrences of double triangles in random planar maps. This is the first result of this kind that goes beyond face counts of given valency. The method is based on generating functions, an involved combinatorial decomposition scheme that leads to a system of catalytic functional equations and an analytic extension of the Quadratic Method to systems of equations.
Cite as

Michael Drmota and Guan-Ru Yu. The Number of Double Triangles in Random Planar Maps. In 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 110, pp. 19:1-19:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{drmota_et_al:LIPIcs.AofA.2018.19,
  author =	{Drmota, Michael and Yu, Guan-Ru},
  title =	{{The Number of Double Triangles in Random Planar Maps}},
  booktitle =	{29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)},
  pages =	{19:1--19:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-078-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{110},
  editor =	{Fill, James Allen and Ward, Mark Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2018.19},
  URN =		{urn:nbn:de:0030-drops-89120},
  doi =		{10.4230/LIPIcs.AofA.2018.19},
  annote =	{Keywords: Planar maps, pattern occuence, generating functions, quadratic method, central limit theorem}
}
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