5 Search Results for "Fang, Wenjie"

Document
DOI: 10.4230/LIPIcs.AofA.2024.3
Maximal Number of Subword Occurrences in a Word

Authors: Wenjie Fang

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

Abstract
We consider the number of occurrences of subwords (non-consecutive sub-sequences) in a given word. We first define the notion of subword entropy of a given word that measures the maximal number of occurrences among all possible subwords. We then give upper and lower bounds of minimal subword entropy for words of fixed length in a fixed alphabet, and also showing that minimal subword entropy per letter has a limit value. A better upper bound of minimal subword entropy for a binary alphabet is then given by looking at certain families of periodic words. We also give some conjectures based on experimental observations.
Cite as

Wenjie Fang. Maximal Number of Subword Occurrences in a Word. 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. 3:1-3:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{fang:LIPIcs.AofA.2024.3,
  author =	{Fang, Wenjie},
  title =	{{Maximal Number of Subword Occurrences in a Word}},
  booktitle =	{35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)},
  pages =	{3:1--3:12},
  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.2024.3},
  URN =		{urn:nbn:de:0030-drops-204387},
  doi =		{10.4230/LIPIcs.AofA.2024.3},
  annote =	{Keywords: Subword occurrence, subword entropy, enumeration, periodic words}
}
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.SEA.2024.20
Targeted Branching for the Maximum Independent Set Problem Using Graph Neural Networks

Authors: Kenneth Langedal, Demian Hespe, and Peter Sanders

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
Identifying a maximum independent set is a fundamental NP-hard problem. This problem has several real-world applications and requires finding the largest possible set of vertices not adjacent to each other in an undirected graph. Over the past few years, branch-and-bound and branch-and-reduce algorithms have emerged as some of the most effective methods for solving the problem exactly. Specifically, the branch-and-reduce approach, which combines branch-and-bound principles with reduction rules, has proven particularly successful in tackling previously unmanageable real-world instances. This progress was largely made possible by the development of more effective reduction rules. Nevertheless, other key components that can impact the efficiency of these algorithms have not received the same level of interest. Among these is the branching strategy, which determines which vertex to branch on next. Until recently, the most widely used strategy was to choose the vertex of the highest degree. In this work, we present a graph neural network approach for selecting the next branching vertex. The intricate nature of current branch-and-bound solvers makes supervised and reinforcement learning difficult. Therefore, we use a population-based genetic algorithm to evolve the model’s parameters instead. Our proposed approach results in a speedup on 73% of the benchmark instances with a median speedup of 24%.
Cite as

Kenneth Langedal, Demian Hespe, and Peter Sanders. Targeted Branching for the Maximum Independent Set Problem Using Graph Neural Networks. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 20:1-20:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{langedal_et_al:LIPIcs.SEA.2024.20,
  author =	{Langedal, Kenneth and Hespe, Demian and Sanders, Peter},
  title =	{{Targeted Branching for the Maximum Independent Set Problem Using Graph Neural Networks}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{20:1--20:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.20},
  URN =		{urn:nbn:de:0030-drops-203853},
  doi =		{10.4230/LIPIcs.SEA.2024.20},
  annote =	{Keywords: Graphs, Independent Set, Vertex Cover, Graph Neural Networks, Branch-and-Reduce}
}
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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