Better Practical Algorithms for rSPR Distance and Hybridization Number

Authors Kohei Yamada, Zhi-Zhong Chen, Lusheng Wang

Thumbnail PDF


  • Filesize: 499 kB
  • 12 pages

Document Identifiers

Author Details

Kohei Yamada
  • Division of Information System Design, Tokyo Denki University, Japan
Zhi-Zhong Chen
  • Division of Information System Design, Tokyo Denki University, Japan
Lusheng Wang
  • Department of Computer Science, City University of Hong Kong, China

Cite AsGet BibTex

Kohei Yamada, Zhi-Zhong Chen, and Lusheng Wang. Better Practical Algorithms for rSPR Distance and Hybridization Number. In 19th International Workshop on Algorithms in Bioinformatics (WABI 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 143, pp. 5:1-5:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


The problem of computing the rSPR distance of two phylogenetic trees (denoted by RDC) is NP-hard and so is the problem of computing the hybridization number of two phylogenetic trees (denoted by HNC). Since they are important problems in phylogenetics, they have been studied extensively in the literature. Indeed, quite a number of exact or approximation algorithms have been designed and implemented for them. In this paper, we design and implement one exact algorithm for HNC and several approximation algorithms for RDC and HNC. Our experimental results show that the resulting exact program is much faster (namely, more than 80 times faster for the easiest dataset used in the experiments) than the previous best and its superiority in speed becomes even more significant for more difficult instances. Moreover, the resulting approximation programs output much better results than the previous bests; indeed, the outputs are always nearly optimal and often optimal. Of particular interest is the usage of the Monte Carlo tree search (MCTS) method in the design of our approximation algorithms. Our experimental results show that with MCTS, we can often solve HNC exactly within short time.

Subject Classification

ACM Subject Classification
  • Theory of computation → Theory and algorithms for application domains
  • phylogenetic tree
  • fixed-parameter algorithms
  • approximation algorithms
  • Monte Carlo tree search


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. B. Albrecht, C. Scornavacca, A. Cenci, and D.H. Huson. Fast computation of minimum hybridization networks. Bioinformatics, 28(2):191-197, 2012. Google Scholar
  2. M. Baroni, C. Semple, and M. Steel. Hybrids in real time. Systematic Biology, 55(1):46-56, 2006. Google Scholar
  3. R.G. Beiko and N. Hamilton. Phylogenetic identification of lateral genetic transfer events. BMC Evolutionary Biology, 6(15):159-169, 2006. Google Scholar
  4. M. Bordewich and C. Semple. On the computational complexity of the rooted subtree prune and regraft distance. Annals of Combinatorics, 8(4):409-423, 2005. Google Scholar
  5. C. Browne, E. Powley, D. Whitehouse, S. Lucas, P.I. Cowling, P. Rohlfshagen, S. Tavener, D. Perez, S. Samothrakis, and S. Colton. A Survey of Monte Carlo Tree Search Methods. IEEE Transactions on Computational Intelligence and AI in Games, 4(1):1-49, 2012. Google Scholar
  6. Z.-Z. Chen, Y. Fan, and L. Wang. Faster exact computation of rSPR distance. Journal of Combinatorial Optimization, 29(3):605-635, 2015. Google Scholar
  7. Z.-Z. Chen, Y. Harada, Y. Nakamura, and L. Wang. Faster exact computation of rSPR distance via better approximation. IEEE/ACM Transactions on Computational Biology and Bioinformatics, to appear. Google Scholar
  8. Z.-Z. Chen, E. Machida, and L. Wang. An Approximation Algorithm for rSPR Distance. In 22nd International Computing and Combinatorics Conference, Ho Chi Minh City, Vietnam, August 2-4, 2016, pages 468-479, 2016. Google Scholar
  9. Z.-Z. Chen and L. Wang. Algorithms for reticulate networks of multiple phylogenetic trees. IEEE/ACM Trans. on Computational Biology and Bioinformatics, 9(2):372-384, 2012. Google Scholar
  10. Z.-Z. Chen and L. Wang. An ultrafast tool for minimum reticulate networks. Journal of Computational Biology, 20(1):38-41, 2013. Google Scholar
  11. L. Collins, S. Linz, and C. Semple. Quantifying hybridization in realistic time. J. of Comput. Biol., 18(10):1305-1318, 2011. Google Scholar
  12. J. Hein, T. Jing, L. Wang, and K. Zhang. On the complexity of comparing evolutionary trees. Disc. Appl. Math., 71(1-3):153-169, 1996. Google Scholar
  13. D.H. Huson, R. Rupp, and C. Scornavacca. Phylogenetic Networks: Concepts, Algorithms and Applications. Cambridge University Press, 2010. Google Scholar
  14. S. Kelk, L. van Iersel, N. Lekic, S. Linz, C. Scornavacca, and L. Stougie. Cycle killer...qu'est-ce que c'est? On the comparative approximability of hybridization number and directed feedback vertex set. SIAM J. Discrete Math., 26(4):1635-1656, 2012. Google Scholar
  15. F. Schalekamp, A. van Zuylen, and S. van der Ster. A Duality Based 2-Approximation Algorithm for Maximum Agreement Forest. In 43rd International Colloquium on Automata, Languages and Programming, Rome, Italy, July 11-15, 2016, pages 70:1-70:14, 2016. Google Scholar
  16. L. van Iersel, S. Kelk, N. Lekic, and C. Scornavacca. A practical approximation algorithm for solving massive instances of hybridization number for binary and nonbinary trees. BMC Bioinformatics, 15(127), 2014. Google Scholar
  17. C. Whidden, R.G. Beiko, and N. Zeh. Fast FPT algorithms for computing rooted agreement forest: theory and experiments. In International Symposium on Experimental Algorithms, Naples, Italy, May 20-22, 2010, pages 141-153, 2010. Google Scholar
  18. C. Whidden, R.G. Beiko, and N. Zeh. Fixed-parameter algorithms for maximum agreement forests. SIAM J. Comput., 42(4):1431-1466, 2013. Google Scholar
  19. C. Whidden and N. Zeh. A unifying view on approximation and FPT of agreement forests. In 9th International Workshop on Algorithms in Bioinformatics, Philadelphia, PA, USA, September 12-13, 2009, pages 390-401, 2009. Google Scholar
  20. Y. Wu. A practical method for exact computation of subtree prune and regraft distance. Bioinformatics, 25(2):190-196, 2009. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail