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Unique Least Common Ancestors and Clusters in Directed Acyclic Graphs

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Algorithms and Discrete Applied Mathematics (CALDAM 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14508))

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Abstract

We investigate the connections between clusters and least common ancestors (LCAs) in directed acyclic graphs (DAGs). We focus on the class of DAGs having unique least common ancestors for certain subsets of their minimal elements since these are of interest, particularly as models of phylogenetic networks. Here, we use the close connection between the canonical k-ary transit function and the closure function on a set system to show that pre-k-ary clustering systems are exactly those that derive from a class of DAGs with unique LCAs. Moreover, we show that k-ary \(\mathscr {T}\)-systems and k-weak hierarchies are associated with DAGs that satisfy stronger conditions on the existence of unique LCAs for sets of size at most k.

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Acknowledgments

AVS acknowledges the financial support from the CSIR-HRDG for the Senior Research Fellowship (09/0102(12336)/2021-EMR-I).

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Authors and Affiliations

  1. Department of Futures Studies, University of Kerala, Trivandrum, 695 581, India

    Ameera Vaheeda Shanavas & Manoj Changat

  2. Department of Mathematics, Faculty of Science, Stockholm University, 10691, Stockholm, Sweden

    Marc Hellmuth

  3. Bioinformatics Group, Department of Computer Science and Interdisciplinary Center for Bioinformatics, Universität Leipzig, Härtelstrasse 16-18, 04107, Leipzig, Germany

    Peter F. Stadler

  4. Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

    Peter F. Stadler

  5. Institute for Theoretical Chemistry, University of Vienna, Vienna, Austria

    Peter F. Stadler

  6. Faculty of Ciencias, Universidad Nacional de Colombia, Bogotá, Colombia

    Peter F. Stadler

  7. Santa Fe Institute, Santa Fe, NM, USA

    Peter F. Stadler

Authors
  1. Ameera Vaheeda Shanavas
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  2. Manoj Changat
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  3. Marc Hellmuth
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  4. Peter F. Stadler
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Corresponding author

Correspondence to Manoj Changat .

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Editors and Affiliations

  1. Indian Institute of Technology Hyderabad, Sangareddy, India

    Subrahmanyam Kalyanasundaram

  2. Carleton University, Ottawa, ON, Canada

    Anil Maheshwari

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Shanavas, A.V., Changat, M., Hellmuth, M., Stadler, P.F. (2024). Unique Least Common Ancestors and Clusters in Directed Acyclic Graphs. In: Kalyanasundaram, S., Maheshwari, A. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2024. Lecture Notes in Computer Science, vol 14508. Springer, Cham. https://doi.org/10.1007/978-3-031-52213-0_11

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  • DOI: https://doi.org/10.1007/978-3-031-52213-0_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-52212-3

  • Online ISBN: 978-3-031-52213-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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