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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Barát, J.: Directed path-width and monotonicity in digraph searching. Graphs Comb. 22(2), 161–172 (2006)
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)
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)
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)
Bryant, D., Lagergren, J.: Compatibility of unrooted phylogenetic trees is FPT. Theor. Comput. Sci. 351(3), 296–302 (2006)
Díaz, J., Petit, J., Serna, M.: A survey of graph layout problems. ACM Comput. Surv. 34(3), 313–356 (2002)
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)
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_6
Huson, D.H., Rupp, R., Scornavacca, C.: Phylogenetic Networks: Concepts: Algorithms and Applications. Cambridge University Press, Cambridge (2010)
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_9
Kelk, S., Scornavacca, C.: Constructing minimal phylogenetic networks from softwired clusters is fixed parameter tractable. Algorithmica 68(4), 886–915 (2014)
Kelk, S., Stamoulis, G., Wu, T.: Treewidth distance on phylogenetic trees. Theor. Comput. Sci. 731, 99–117 (2018)
Rabier, C.E., Berry, V., Pardi, F., Scornavacca, C.: On the inference of complicated phylogenetic networks by Markov chain Monte-Carlo (submitted)
Sethi, R.: Complete register allocation problems. SIAM J. Comput. 4(3), 226–248 (1975)
Whidden, C., Beiko, R.G., Zeh, N.: Fixed-parameter algorithms for maximum agreement forests. SIAM J. Comput. 42(4), 1431–1466 (2013)
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)
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).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Berry, V., Scornavacca, C., Weller, M. (2020). Scanning Phylogenetic Networks Is NP-hard. In: Chatzigeorgiou, A., et al. SOFSEM 2020: Theory and Practice of Computer Science. SOFSEM 2020. Lecture Notes in Computer Science(), vol 12011. Springer, Cham. https://doi.org/10.1007/978-3-030-38919-2_42
Download citation
DOI: https://doi.org/10.1007/978-3-030-38919-2_42
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-38918-5
Online ISBN: 978-3-030-38919-2
eBook Packages: Computer ScienceComputer Science (R0)