3 Search Results for "Elvey Price, Andrew"

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.2024.15
Asymptotics of Relaxed k-Ary Trees

Authors: Manosij Ghosh Dastidar and Michael Wallner

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

Abstract
A relaxed k-ary tree is an ordered directed acyclic graph with a unique source and sink in which every node has out-degree k. These objects arise in the compression of trees in which some repeated subtrees are factored and repeated appearances are replaced by pointers. We prove an asymptotic theta-result for the number of relaxed k-ary tree with n nodes for n → ∞. This generalizes the previously proved binary case to arbitrary finite arity, and shows that the seldom observed phenomenon of a stretched exponential term e^{c n^{1/3}} appears in all these cases. We also derive the recurrences for compacted k-ary trees in which all subtrees are unique and minimal deterministic finite automata accepting a finite language over a finite alphabet.
Cite as

Manosij Ghosh Dastidar and Michael Wallner. Asymptotics of Relaxed k-Ary Trees. 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. 15:1-15:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ghoshdastidar_et_al:LIPIcs.AofA.2024.15,
  author =	{Ghosh Dastidar, Manosij and Wallner, Michael},
  title =	{{Asymptotics of Relaxed k-Ary Trees}},
  booktitle =	{35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)},
  pages =	{15:1--15:13},
  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.2024.15},
  URN =		{urn:nbn:de:0030-drops-204506},
  doi =		{10.4230/LIPIcs.AofA.2024.15},
  annote =	{Keywords: Asymptotic enumeration, stretched exponential, Airy function, directed acyclic graph, Dyck paths, compacted trees, minimal automata}
}
Document
DOI: 10.4230/LIPIcs.AofA.2020.11
Asymptotics of Minimal Deterministic Finite Automata Recognizing a Finite Binary Language

Authors: Andrew Elvey Price, Wenjie Fang, and Michael Wallner

Published in: LIPIcs, Volume 159, 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020)

Abstract
We show that the number of minimal deterministic finite automata with n+1 states recognizing a finite binary language grows asymptotically for n → ∞ like Θ(n! 8ⁿ e^{3 a₁ n^{1/3}} n^{7/8}), where a₁ ≈ -2.338 is the largest root of the Airy function. For this purpose, we use a new asymptotic enumeration method proposed by the same authors in a recent preprint (2019). We first derive a new two-parameter recurrence relation for the number of such automata up to a given size. Using this result, we prove by induction tight bounds that are sufficiently accurate for large n to determine the asymptotic form using adapted Netwon polygons.
Cite as

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 (AofA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 159, pp. 11:1-11:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{elveyprice_et_al:LIPIcs.AofA.2020.11,
  author =	{Elvey Price, Andrew and Fang, Wenjie and Wallner, Michael},
  title =	{{Asymptotics of Minimal Deterministic Finite Automata Recognizing a Finite Binary Language}},
  booktitle =	{31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020)},
  pages =	{11:1--11:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-147-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{159},
  editor =	{Drmota, Michael and Heuberger, Clemens},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2020.11},
  URN =		{urn:nbn:de:0030-drops-120419},
  doi =		{10.4230/LIPIcs.AofA.2020.11},
  annote =	{Keywords: Airy function, asymptotics, directed acyclic graphs, Dyck paths, bijection, stretched exponential, compacted trees, minimal automata, finite languages}
}
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