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On the Parameterized Complexity of the Perfect Phylogeny Problem

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SOFSEM 2024: Theory and Practice of Computer Science (SOFSEM 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14519))

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Abstract

This paper categorizes the parameterized complexity of the algorithmic problems Perfect Phylogeny and Triangulating Colored Graphs when parameterized by the number of genes and colors, respectively. We show that they are complete for the parameterized complexity class XALP using a reduction from Tree-chained Multicolor Independent Set and a proof of membership. We introduce the problem Triangulating Multicolored Graphs as a stepping stone and prove XALP-completeness for this problem as well. We also show that, assuming the Exponential Time Hypothesis, there exists no algorithm that solves any of these problems in time \(f(k)n^{o(k)}\), where n is the input size, k the parameter, and f any computable function.

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Acknowledgements

This paper was written as a master thesis at Utrecht University. I wish to thank my supervisors Hans L. Bodlaender and Carla Groenland for the discussions and guidance.

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Authors and Affiliations

  1. Utrecht University, Utrecht, The Netherlands

    Jorke M. de Vlas

  2. Linköping Universitet, Linköping, Sweden

    Jorke M. de Vlas

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  1. Jorke M. de Vlas
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Correspondence to Jorke M. de Vlas .

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Editors and Affiliations

  1. University of Trier, Trier, Germany

    Henning Fernau

  2. UNSW Sydney, Sydney, NSW, Australia

    Serge Gaspers

  3. CNRS and University of Bordeaux, Talence, France

    Ralf Klasing

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de Vlas, J.M. (2024). On the Parameterized Complexity of the Perfect Phylogeny Problem. In: Fernau, H., Gaspers, S., Klasing, R. (eds) SOFSEM 2024: Theory and Practice of Computer Science. SOFSEM 2024. Lecture Notes in Computer Science, vol 14519. Springer, Cham. https://doi.org/10.1007/978-3-031-52113-3_12

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  • DOI: https://doi.org/10.1007/978-3-031-52113-3_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-52112-6

  • Online ISBN: 978-3-031-52113-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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