Reconstructing Phylogenetic Tree From Multipartite Quartet System

Authors Hiroshi Hirai, Yuni Iwamasa

Thumbnail PDF


  • Filesize: 1.85 MB
  • 13 pages

Document Identifiers

Author Details

Hiroshi Hirai
  • Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, Japan
Yuni Iwamasa
  • Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, Japan

Cite AsGet BibTex

Hiroshi Hirai and Yuni Iwamasa. Reconstructing Phylogenetic Tree From Multipartite Quartet System. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 57:1-57:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


A phylogenetic tree is a graphical representation of an evolutionary history in a set of taxa in which the leaves correspond to taxa and the non-leaves correspond to speciations. One of important problems in phylogenetic analysis is to assemble a global phylogenetic tree from smaller pieces of phylogenetic trees, particularly, quartet trees. Quartet Compatibility is to decide 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 but 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. We also see that complete/full multipartite quartet systems naturally arise from a limited situation of block-restricted measurement.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial algorithms
  • phylogenetic tree
  • quartet system
  • reconstruction


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


  1. A. V. Aho, Y. Sagiv, T. G. Szymanski, and J. D. Ullman. Inferring a tree from lowest common ancestors with an application to the optimization of relational expressions. SIAM Journal on Computing, 10(3):405-421, 1981. Google Scholar
  2. H.-J. Bandelt and A. Dress. Reconstructing the shape of a tree from observed dissimilarity data. Advances in Applied Mathematics, 7:309-343, 1986. Google Scholar
  3. V. Berry, D. Bryant, T. Jiang, P. Kearney, M. Li, T. Wareham, and H. Zhang. A practical algorithm for recovering the best supported edges of an evolutionary tree. In Proceedings of the 11th ACM-SIAM Symposium on Discrete Algorithms (SODA'00), pages 287-296, 2000. Google Scholar
  4. V. Berry, T. Jiang, P. Kearney, M. Li, and T. Wareham. Quartet cleaning: Improved algorithms and simulations. In Proceedings of the 7th European Symposium on Algorithm (ESA'99), volume 1643 of Lecture Notes in Computer Science, pages 313-324, Heidelberg, 1999. Springer. Google Scholar
  5. D. Bryant and M. Steel. Extension operations on sets of leaf-labelled trees. Advances in Applied Mathematics, 16:425-453, 1995. Google Scholar
  6. P. Buneman. The recovery of trees from measures of dissimilarity. In F. R. Hodson, D. G. Kendall, and P. Tautu, editors, Mathematics in the Archaeological and Historical Science, pages 387-395. Edinburgh University Press, 1971. Google Scholar
  7. M.-S Chang, C.-C Lin, and P. Rossmanith. New fixed-parameter algorithms for the minimum quartet inconsistency problem. Theory of Computing Systems, 47(2):342-367, 2010. Google Scholar
  8. H. Colonius and H. H. Schulze. Tree structure from proximity data. British Journal of Mathematical and Statistical Psychology, 34:167-180, 1981. Google Scholar
  9. W. M. Fitch. A non-sequential method for constructing trees and hierarchical classifications. Journal of Molecular Evolution, 18:30-37, 1981. Google Scholar
  10. J. Gramm and R. Niedermeier. A fixed-parameter algorithm for minimum quartet inconsistency. Journal of Computer and System Sciences, 67:723-741, 2003. Google Scholar
  11. H. Hirai, Y. Iwamasa, K. Murota, and S. Živný. A tractable class of binary VCSPs via M-convex intersection. arXiv, 2018. URL:
  12. T. Jiang, P. Kearney, and M. Li. A polynomial time approximation scheme for inferring evolutionary trees from quartet topologies and its application. SIAM Journal on Computing, 30(6):1942-1961, 2001. Google Scholar
  13. R. Reaz, M. S. Bayzid, and M. S. Rahman. Accurate phylogenetic tree reconstruction from quartets: A heuristic approach. PLoS ONE, 9(8):e104008, 2014. Google Scholar
  14. S. Sattath and A. Tversky. Additive similarity trees. Psychometrika, 42(319-345), 1977. Google Scholar
  15. A. Schrijver. Combinatorial Optimization: Polyhedra and Efficiency. Springer, Heidelberg, 2003. Google Scholar
  16. C. Semple and M. Steel. A supertree method for rooted trees. Discrete Applied Mathematics, 105:147-158, 2000. Google Scholar
  17. C. Semple and M. Steel. Phylogenetics. Oxford University Press, Oxford, 2003. Google Scholar
  18. M. Steel. The complexity of reconstructing trees from qualitative characters and subtrees. Journal of Classification, 9:91-116, 1992. Google Scholar
  19. K. Strimmer and A. Haeseler. Quartet puzzling: A quartet maximum-likelihood method for reconstructing tree topologies. Journal of Molecular Biology and Evolution, 13:964-969, 1996. 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