A Unifying View on Approximation and FPT of Agreement Forests

(Extended Abstract)
  • Chris Whidden
  • Norbert Zeh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5724)


We provide a unifying view on the structure of maximum (acyclic) agreement forests of rooted and unrooted phylogenies. This enables us to obtain linear- or O(n log n)-time 3-approximation and improved fixed-parameter algorithms for the subtree prune and regraft distance between two rooted phylogenies, the tree bisection and reconnection distance between two unrooted phylogenies, and the hybridization number of two rooted phylogenies.


Sibling Pair Recursive Call Unify View Agreement Forest Hybridization Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Allen, B.L., Steel, M.: Subtree transfer operations and their induced metrics on evolutionary trees. Annals of Comb. 5, 1–15 (2001)CrossRefGoogle Scholar
  2. 2.
    Baroni, M., Grünewald, S., Moulton, V., Semple, C.: Bounding the number of hybridisation events for a consistent evolutionary history. J. Math. Biol. 51, 171–182 (2005)CrossRefPubMedGoogle Scholar
  3. 3.
    Beiko, R.G., Hamilton, N.: Phylogenetic identification of lateral genetic transfer events. BMC Evol. Biol. 6, 15 (2006)CrossRefPubMedPubMedCentralGoogle Scholar
  4. 4.
    Bonet, M.L., St. John, K., Mahindru, R., Amenta, N.: Approximating subtree distances between phylogenies. J. Comp. Biol. 13, 1419–1434 (2006)CrossRefGoogle Scholar
  5. 5.
    Bordewich, M., McCartin, C., Semple, C.: A 3-approximation algorithm for the subtree distance between phylogenies. J. Disc. Alg. 6, 458–471 (2008)CrossRefGoogle Scholar
  6. 6.
    Bordewich, M., Semple, C.: On the computational complexity of the rooted subtree prune and regraft distance. Annals of Comb. 8, 409–423 (2005)CrossRefGoogle Scholar
  7. 7.
    Bordewich, M., Semple, C.: Computing the hybridization number of two phylogenetic trees is fixed-parameter tractable. IEEE/ACM Trans. on Comp. Biol. and Bioinf. 4, 458–466 (2007)CrossRefGoogle Scholar
  8. 8.
    Bordewich, M., Semple, C.: Computing the minimum number of hybridization events for a consistent evolutionary history. Disc. Appl. Math. 155, 914–928 (2007)CrossRefGoogle Scholar
  9. 9.
    Chataigner, F.: Approximating the maximum agreement forest on k trees. Inf. Proc. Letters 93, 239–244 (2005)CrossRefGoogle Scholar
  10. 10.
    Hallett, M., McCartin, C.: A faster FPT algorithm for the maximum agreement forest problem. Theory of Comp. Sys. 41, 539–550 (2007)CrossRefGoogle Scholar
  11. 11.
    Hein, J., Jiang, T., Wang, L., Zhang, K.: On the complexity of comparing evolutionary trees. Disc. Appl. Math. 71, 153–169 (1996)CrossRefGoogle Scholar
  12. 12.
    Hickey, G., Dehne, F., Rau-Chaplin, A., Blouin, C.: SPR distance computation for unrooted trees. Evol. Bioinf. 4, 17–27 (2008)Google Scholar
  13. 13.
    Hillis, D.M., Heath, T.A., St. John, K.: Analysis and visualization of tree space. Syst. Biol. 54, 471–482 (2005)CrossRefPubMedGoogle Scholar
  14. 14.
    Hillis, D.M., Moritz, C., Mable, B.K. (eds.): Molecular Systematics. Sinauer Associates (1996)Google Scholar
  15. 15.
    Maddison, W.P.: Gene trees in species trees. Syst. Biol. 46, 523–536 (1997)CrossRefGoogle Scholar
  16. 16.
    Nakhleh, L., Warnow, T., Lindner, C.R., St. John, K.: Reconstructing reticulate evolution in species—theory and practice. J. Comp. Biol. 12, 796–811 (2005)CrossRefGoogle Scholar
  17. 17.
    Rodrigues, E.M., Sagot, M.-F., Wakabayashi, Y.: The maximum agreement forest problem: Approximation algorithms and computational experiments. Theor. Comp. Sci. 374, 91–110 (2007)CrossRefGoogle Scholar
  18. 18.
    Whidden, C., Zeh, N.: A unifying view on approximation and FPT of agreement forests (2009),

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Chris Whidden
    • 1
  • Norbert Zeh
    • 1
  1. 1.Faculty of Computer ScienceDalhousie UniversityHalifaxCanada

Personalised recommendations