Improved Approximation Algorithm for Maximum Agreement Forest of Two Trees

  • Feng Shi
  • Jie You
  • Qilong Feng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8497)


Given two rooted binary phylogenetic trees with identical leaf label-set, the Maximum Agreement Forest (Maf) problem asks for a largest common subforest of these two trees. This problem is known to be NP-complete and MAX SNP-hard, and the previously best approximation algorithm for this problem has a ratio 3. In this paper, we present an improved 2.5-approximation algorithm for the Maf problem on two rooted binary phylogenetic trees.


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  1. 1.
    Robinson, D., Foulds, L.: Comparison of phylogenetic trees. Mathematical Biosciences 53(1-2), 131–147 (1981)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Li, M., Tromp, J., Zhang, L.: On the nearest neighbour interchange distance between evolutionary trees. Journal on Theoretical Biology 182(4), 463–467 (1996)CrossRefGoogle Scholar
  3. 3.
    Hodson, F., Kendall, D., Tauta, P. (eds.): The recovery of trees from measures of dissimilarity. Mathematics in the Archaeological and Historical Sciences, pp. 387–395. Edinburgh University Press, Edinburgh (1971)Google Scholar
  4. 4.
    Swofford, D., Olsen, G., Waddell, P., Hillis, D.: Phylogenetic inference. In: Molecular Systematics, 2nd edn., pp. 407–513. Sinauer, Associates (1996)Google Scholar
  5. 5.
    Hein, J., Jiang, T., Wang, L., Zhang, K.: On the complexity of comparing evolutionary trees. Discrete Applied Mathematics 71, 153–169 (1996)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Bordewich, M., Semple, C.: On the computational complexity of the rooted subtree prune and regraft distance. Annals of Combinatorics 8(4), 409–423 (2005)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Rodrigues, E.M., Sagot, M.-F., Wakabayashi, Y.: Some approximation results for the maximum agreement forest problem. In: Goemans, M.X., Jansen, K., Rolim, J.D.P., Trevisan, L. (eds.) RANDOM 2001 and APPROX 2001. LNCS, vol. 2129, pp. 159–169. Springer, Heidelberg (2001)Google Scholar
  8. 8.
    Bonet, M., John, R., Mahindru, R., Amenta, N.: Approximating subtree distances between phylogenies. J. Comput. Biol. 13(8), 1419–1434 (2006)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Bordewich, M., McCartin, C., Semple, C.: A 3-approximation algorithm for the subtree distance between phylogenies. J. Discrete Algorithms 6(3), 458–471 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Rodrigues, E., Sagot, M., Wakabayashi, Y.: The maximum agreement forest problem: approximation algorithms and computational experiments. Theoretical Computer Science 374(1-3), 91–110 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Whidden, C., Zeh, N.: A unifying view on approximation and FPT of agreement forests. In: Salzberg, S.L., Warnow, T. (eds.) WABI 2009. LNCS, vol. 5724, pp. 390–402. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  12. 12.
    Whidden, C., Beiko, R., Zeh, N.: Fixed-parameter and approximation algorithms for maximum agreement forests. CoRR. abs/1108.2664 (2011)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Feng Shi
    • 1
  • Jie You
    • 1
  • Qilong Feng
    • 1
  1. 1.School of Information Science and EngineeringCentral South UniversityChina

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