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Scanning Phylogenetic Networks Is NP-hard

  • Vincent Berry
  • Celine Scornavacca
  • Mathias WellerEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12011)

Abstract

Phylogenetic networks are rooted directed acyclic graphs used to depict the evolution of a set of species in the presence of reticulate events. Reconstructing these networks from molecular data is challenging and current algorithms fail to scale up to genome-wide data. In this paper, we introduce a new width measure intended to help design faster parameterized algorithms for this task. We study its relation with other width measures and problems in graph theory and finally prove that deciding it is NP-complete, even for very restricted classes of networks.

Notes

Acknowledgments

We thank Fabio Pardi to have brought the problem to our attention and the Genome Harvest project, ref. ID 1504-006 (“Investissements d’avenir”, ANR-10-LABX-0001-01).

References

  1. 1.
    Barát, J.: Directed path-width and monotonicity in digraph searching. Graphs Comb. 22(2), 161–172 (2006)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bordewich, M., Scornavacca, C., Tokac, N., Weller, M.: On the fixed parameter tractability of agreement-based phylogenetic distances. J. Math. Biol. 74(1), 239–257 (2017)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bordewich, M., Semple, C.: Computing the hybridization number of two phylogenetic trees is fixed-parameter tractable. IEEE/ACM Trans. Comput. Biol. Bioinform. 4(3), 458–466 (2007)CrossRefGoogle Scholar
  4. 4.
    Bryant, D., Bouckaert, R., Felsenstein, J., Rosenberg, N.A., RoyChoudhury, A.: Inferring species trees directly from biallelic genetic markers: bypassing gene trees in a full coalescent analysis. Mol. Biol. Evol. 29(8), 1917–1932 (2012)CrossRefGoogle Scholar
  5. 5.
    Bryant, D., Lagergren, J.: Compatibility of unrooted phylogenetic trees is FPT. Theor. Comput. Sci. 351(3), 296–302 (2006)CrossRefGoogle Scholar
  6. 6.
    Díaz, J., Petit, J., Serna, M.: A survey of graph layout problems. ACM Comput. Surv. 34(3), 313–356 (2002)CrossRefGoogle Scholar
  7. 7.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman & Co., Ltd., New York City (1979)zbMATHGoogle Scholar
  8. 8.
    Grigoriev, A., Kelk, S., Lekić, N.: On low treewidth graphs and supertrees. In: Dediu, A.-H., Martín-Vide, C., Truthe, B. (eds.) AlCoB 2014. LNCS, vol. 8542, pp. 71–82. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-07953-0_6CrossRefGoogle Scholar
  9. 9.
    Huson, D.H., Rupp, R., Scornavacca, C.: Phylogenetic Networks: Concepts: Algorithms and Applications. Cambridge University Press, Cambridge (2010)CrossRefGoogle Scholar
  10. 10.
    Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W., Bohlinger, J.D. (eds.) Complexity of Computer Computations. The IBM Research Symposia Series, pp. 85–103. Springer, Boston (1972).  https://doi.org/10.1007/978-1-4684-2001-2_9CrossRefGoogle Scholar
  11. 11.
    Kelk, S., Scornavacca, C.: Constructing minimal phylogenetic networks from softwired clusters is fixed parameter tractable. Algorithmica 68(4), 886–915 (2014)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Kelk, S., Stamoulis, G., Wu, T.: Treewidth distance on phylogenetic trees. Theor. Comput. Sci. 731, 99–117 (2018)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Rabier, C.E., Berry, V., Pardi, F., Scornavacca, C.: On the inference of complicated phylogenetic networks by Markov chain Monte-Carlo (submitted)Google Scholar
  14. 14.
    Sethi, R.: Complete register allocation problems. SIAM J. Comput. 4(3), 226–248 (1975)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Whidden, C., Beiko, R.G., Zeh, N.: Fixed-parameter algorithms for maximum agreement forests. SIAM J. Comput. 42(4), 1431–1466 (2013)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Zhang, C., Ogilvie, H.A., Drummond, A.J., Stadler, T.: Bayesian inference of species networks from multilocus sequence data. Mol. Biol. Evol. 35(2), 504–517 (2018)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Vincent Berry
    • 1
  • Celine Scornavacca
    • 2
  • Mathias Weller
    • 3
    Email author
  1. 1.LIRMM, Université de MontpellierMontpellierFrance
  2. 2.CNRS, Université de MontpellierMontpellierFrance
  3. 3.CNRS, LIGM, Université Paris EstMarne-la-ValléeFrance

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