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Reconstructing Phylogenetic Trees from Multipartite Quartet Systems

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Abstract

A phylogenetic tree is a graphical representation of an evolutionary history of taxa in which the leaves correspond to the taxa and the non-leaves correspond to speciations. One of important problems in phylogenetic analysis is to assemble a global phylogenetic tree from small phylogenetic trees, particularly, quartet trees. Quartet Compatibility is the problem of deciding whether there is a phylogenetic tree inducing a given collection of quartet trees, and to construct such a phylogenetic tree if it exists. It is known that Quartet Compatibility is NP-hard and that there are only a few results known for polynomial-time solvable subclasses. In this paper, we introduce two novel classes of quartet systems, called complete multipartite quartet system and full multipartite quartet system, and present polynomial-time algorithms for Quartet Compatibility for these systems.

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Acknowledgements

We thank Kunihiko Sadakane for bibliographical information. The first author is supported by JSPS KAKENHI Grant Numbers JP26280004, JP17K00029. The second author is supported by JSPS KAKENHI Grant Numbers JP16J04545, JP17K00029, JP19J01302, 20K23323, 20H05795, Japan.

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Authors and Affiliations

  1. Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, 113-8656, Japan

    Hiroshi Hirai

  2. Department of Communications and Computer Engineering, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

    Yuni Iwamasa

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  1. Hiroshi Hirai
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  2. Yuni Iwamasa
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Correspondence to Yuni Iwamasa.

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A preliminary version of this paper has appeared in the proceedings of the 29th International Symposium on Algorithms and Computation (ISAAC 2018).

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Hirai, H., Iwamasa, Y. Reconstructing Phylogenetic Trees from Multipartite Quartet Systems. Algorithmica 84, 1875–1896 (2022). https://doi.org/10.1007/s00453-022-00945-9

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