Constructing Parsimonious Hybridization Networks from Multiple Phylogenetic Trees Using a SAT-Solver

  • Vladimir UlyantsevEmail author
  • Mikhail Melnik
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9199)


We present an exact algorithm for constructing minimal hybridization networks from multiple trees which is based on reducing the problem to the Boolean satisfiability problem. The main idea of our algorithm is to iterate over possible hybridization numbers and to construct a Boolean formula for each of them that is satisfiable iff there exists a network with such hybridization number. The proposed algorithm is implemented in a software tool PhyloSAT. The experimental evaluation of our algorithm on biological data shows that our method is as far as we know the fastest exact algorithm for the minimal hybridization network construction problem.


Phylogenetic networks Boolean satisfiability SAT Bioinformatics Genetics 



This work was financially supported by the Government of Russian Federation, Grant 074-U01. Authors would like to thank Igor Buzhinsky, Daniil Chivilikhin and Fedor Tsarev for helpful comments and conversations.


  1. 1.
    Biere, A., Cimatti, A., Clarke, E.M., Strichman, O., Zhu, Y.: Bounded model checking. Adv. Comput. 58, 117–148 (2003)CrossRefGoogle Scholar
  2. 2.
    Bonet, M.L., John, K.S.: Efficiently calculating evolutionary tree measures using SAT. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 4–17. Springer, Heidelberg (2009) CrossRefGoogle Scholar
  3. 3.
    Bordewich, M., Semple, C.: Computing the minimum number of hybridization events for a consistent evolutionary history. Discret. Appl. Math. 155(8), 914–928 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Chen, Z.Z., Wang, L.: Hybridnet: a tool for constructing hybridization networks. Bioinform. 26(22), 2912–2913 (2010)CrossRefGoogle Scholar
  5. 5.
    Heule, M.J.H., Verwer, S.: Exact DFA identification using SAT solvers. In: Sempere, J.M., García, P. (eds.) ICGI 2010. LNCS, vol. 6339, pp. 66–79. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  6. 6.
    Hölldobler, S., Nguyen, V.: An efficient encoding of the at-most-one constraint. Technical report, KRR Group 2013–04, Technische Universität Dresden, 01062 Dresden, Germany (2013)Google Scholar
  7. 7.
    Huson, D.H., Rupp, R., Scornavacca, C.: Phylogenetic Networks: Concepts, Algorithms and Applications. Cambridge University Press, New York (2010) CrossRefGoogle Scholar
  8. 8.
    Morrison, D.A.: Introduction to Phylogenetic Networks. RJR Productions, Uppsala (2011)Google Scholar
  9. 9.
    Nakhleh, L.: Evolutionary phylogenetic networks: models and issues. In: Heath, L.S., Ramakrishnan, H. (eds.) Problem Solving Handbook in Computational Biology and Bioinformatics, pp. 125–158. Springer, Berlin (2011)Google Scholar
  10. 10.
    Nakhleh, L., Ruths, D., Wang, L.-S.: RIATA-HGT: a fast and accurate heuristic for reconstructing horizontal gene transfer. In: Wang, L. (ed.) COCOON 2005. LNCS, vol. 3595, pp. 84–93. Springer, Heidelberg (2005) CrossRefGoogle Scholar
  11. 11.
    Park, H.J., Nakhleh, L.: MURPAR: a fast heuristic for inferring parsimonious phylogenetic networks from multiple gene trees. In: Bleris, L., Măndoiu, I., Schwartz, R., Wang, J. (eds.) ISBRA 2012. LNCS, vol. 7292, pp. 213–224. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  12. 12.
    Semple, C.: Hybridization Networks. Department of Mathematics and Statistics, University of Canterbury, New York (2006) Google Scholar
  13. 13.
    Wu, Y.: Close lower and upper bounds for the minimum reticulate network of multiple phylogenetic trees. Bioinformat. 26(12), i140–i148 (2010)CrossRefGoogle Scholar
  14. 14.
    Wu, Y.: An algorithm for constructing parsimonious hybridization networks with multiple phylogenetic trees. J. Comput. Biol. 20(10), 792–804 (2013)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.ITMO UniversitySaint PetersburgRussia

Personalised recommendations