A fixed-parameter algorithm for the maximum agreement forest problem on multifurcating trees

多叉树最大一致森林问题参数算法研究

Abstract

The Maximum Agreement Forest (MAF) problem on two given phylogenetic trees is an important NP-hard problem in the field of computational biology. In this paper, we study the parameterized version of the MAF problem: given two unrooted (multifurcating) phylogenetic trees T 1 and T 2 with the same leaf-label set L, and a parameter k, either construct an agreement forest of at most k trees for T 1 and T 2, or report that no such a forest exists. Whether there is a fixed-parameter tractable algorithm for this problem was posed as an open problem several times in the literature. In this paper, we resolve this open problem by presenting a parameterized algorithm of running time O(4k n 5) for the problem.

创新点

两棵系统发生树的最大一致森林问题在计算生物学领域中是一个非常重要的NP难解问题。本文对参数化的最大一致森林问题进行了研究:给定两棵拥有相同叶子标签集合的无根多叉系统发生树T1和T2,以及一个参数k,问T1和T2是否存在一个一致森林,其包含的树的棵数不超过k,如存在请返回这样的一个一致森林,如不存在请回答不存在。在相关文献中,此问题是否固定参数可解作为开放性问题被提出。本文对该问题提出了一个时间复杂度为O(4^k n^5)的参数算法,证明了此问题是固定参数可解的。

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References

  1. 1

    Hillis D M. Predictive evolution. Science, 1999, 286: 1866–1867

    Article  Google Scholar 

  2. 2

    Ding Z, Filkov V, Gusfield D. A linear-time algorithm for the perfect phylogeny haplotyping (PPH) problem. In: Proceedings of 9th Annual International Conference of Research in Computational Molecular Biology (RECOMB 2005), Cambridge, 2005. 585–600

    Google Scholar 

  3. 3

    Warnow T, Ringe D, Taylor A. Reconstructing the evolutionary history of natural languages. In: Proceedings of 7th ACM-SIAM Symposium on Discrete Algorithms (SODA 1996), Atlanta, 1996. 314–322

    Google Scholar 

  4. 4

    Robinson D F, Foulds L R. Comparison of phylogenetic trees. Math Biosci, 1981, 53: 131–147

    MathSciNet  Article  MATH  Google Scholar 

  5. 5

    Li M, Tromp J, Zhang L. On the nearest neighbour interchange distance between evolutionary trees. J Theor Biol, 1996, 182: 463–467

    Article  Google Scholar 

  6. 6

    Das Gupta B, He X, Jiang T, et al. On distances between phylogenetic trees. In: Proceedings of 8th ACM-SIAM Symposium of Discrete Algorithms (SODA 1997), New Orleans, 1997. 427–436

    Google Scholar 

  7. 7

    Swofford D, Olsen G, Waddell P, et al Phylogenetic inference. In: Hillis D, Moritz C, Mable B, eds. Molecular Systematics. 2nd ed. Sunderland: Sinauer Associates, 1996. 407–513

    Google Scholar 

  8. 8

    Hein J, Jiang T, Wang L, et al. On the complexity of comparing evolutionary trees. Discrete Appl Math, 1996, 71: 153–169

    MathSciNet  Article  MATH  Google Scholar 

  9. 9

    Allen B L, Steel M. Subtree transfer operations and their induced metrics on evolutionary trees. Ann Comb, 2001, 5: 1–15

    MathSciNet  Article  MATH  Google Scholar 

  10. 10

    Bordewich M, Semple C. On the computational complexity of the rooted subtree prune and regraft distance. Ann Comb, 2005, 8: 409–423

    MathSciNet  Article  MATH  Google Scholar 

  11. 11

    Hickey G, Dehne F, Rau-Chaplin A, et al. SPR distance computation for unrooted trees. Evol Bioinform Online, 2008, 4: 17

    Google Scholar 

  12. 12

    Baroni M, Grnewald S, Moulton V, et al. Bounding the number of hybridisation events for a consistent evolutionary history. J Math Biol, 2005, 51: 171–182

    MathSciNet  Article  MATH  Google Scholar 

  13. 13

    Chen J E, Feng Q L. On unknown small subsets and implicit measures: new techniques for parameterized algorithms. J Comput Sci Technol, 2014, 29: 870–878

    MathSciNet  Article  Google Scholar 

  14. 14

    Feng Q L, Wang J X, Li S H, et al. Randomized parameterized algorithms for P2-Packing and Co-Path Packing problems. J Comb Optim, 2015, 29: 125–140

    MathSciNet  Article  MATH  Google Scholar 

  15. 15

    Feng Q L, Wang J X, Chen J E. Matching and weighted P2-Packing: algorithms and kernels. Theor Comput Sci, 2014, 522: 85–94

    MathSciNet  Article  MATH  Google Scholar 

  16. 16

    Feng Q L, Wang J X, Xu C, et al. Improved parameterized algorithms for minimum link-length rectilinear spanning path problem. Theor Comput Sci, 2014, 560: 158–171

    MathSciNet  Article  MATH  Google Scholar 

  17. 17

    Wang J X, Tan P Q, Yao J Y, et al. On the minimum link-length rectilinear spanning path problem: complexity and algorithms. IEEE Trans Comput, 2014, 63: 3092–3100

    MathSciNet  Article  Google Scholar 

  18. 18

    Wang J X, Li W J, Li S H, et al. On the parameterized vertex cover problem for graphs with perfect matching. Sci China Inf Sci, 2014, 57: 072107

    MathSciNet  MATH  Google Scholar 

  19. 19

    Downy R, Fellows M. Parameterized Complexity. New York: Springer-Verlag, 1999

    Google Scholar 

  20. 20

    Hallett M, Mccartin C. A faster FPT algorithm for the maximum agreement forest problem. Theory Comput Syst, 2007, 41: 539–550

    MathSciNet  Article  MATH  Google Scholar 

  21. 21

    Whidden C, Zeh N. A Unifying View on Approximation and FPT of Agreement Forests. Berlin/Heidelberg: Springer, 2009

    Google Scholar 

  22. 22

    Linz S, Semple C. Hybridization in nonbinary trees. IEEE/ACM Trans Comput Biol Bioinform, 2009, 6: 30–45

    Article  Google Scholar 

  23. 23

    Whidden C, Beiko R G, Zeh N. Fixed-parameter and approximation algorithms for maximum agreement forests. arXiv preprint, arXiv:1108.2664, 2011

    Google Scholar 

  24. 24

    Paun O, Lehnebach C, Johansson J T, et al. Phylogenetic relationships and biogeography of Ranunculus and allied genera (Ranunculaceae) in the Mediterranean region and in the European alpine system. Taxon, 2005, 54: 911–932

    Article  Google Scholar 

  25. 25

    Willyard A, Wallace L E, Wagner W L, et al. Estimating the species tree for Hawaiian Schiedea (Caryophyllaceae) from multiple loci in the presence of reticulate evolution. Mol Phylogenet Evol, 2011, 60: 29–48

    Article  Google Scholar 

  26. 26

    Maddison W. Reconstructing character evolution on polytomous cladograms. Cladistics, 1989, 5: 365–377

    Article  Google Scholar 

  27. 27

    Whelan S, Money D. The prevalence of multifurcations in tree-space and their implications for tree-search. Mol Biol Evol, 2010, 27: 2674–2677

    Article  Google Scholar 

  28. 28

    Beiko R G, Hamilton N. Phylogenetic identification of lateral genetic transfer events. BMC Evol Biol, 2006, 6: 15

    Article  Google Scholar 

  29. 29

    Rodrigues E M, Sagot M F, Wakabayashi Y. The maximum agreement forest problem: approximation algorithms and computational experiments. Theor Comput Sci, 2007, 374: 91–110

    MathSciNet  Article  MATH  Google Scholar 

  30. 30

    Buneman P. The recovery of trees from measures of issimilarity. In: Hodson F, Kendall D, Tauta P, eds. Mathematics in the Archaeological and Historical Sciences. Edinburgh: Edinburgh University Press, 1971. 387–395

    Google Scholar 

  31. 31

    Chen J E, Fan J H, Sze S H. Parameterized and approximation algorithms for maximum agreement forest in multifurcating trees. Theor Comput Sci, 2015, 562: 496–512

    MathSciNet  Article  MATH  Google Scholar 

  32. 32

    Shi F, Wang J, Chen J E, et al. Algorithms for parameterized maximum agreement forest problem on multiple trees. Theor Comput Sci, 2014, 554: 207–216

    MathSciNet  Article  MATH  Google Scholar 

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Correspondence to Jianxin Wang.

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Shi, F., Wang, J., Yang, Y. et al. A fixed-parameter algorithm for the maximum agreement forest problem on multifurcating trees. Sci. China Inf. Sci. 59, 1–14 (2016). https://doi.org/10.1007/s11432-015-5355-1

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Keywords

  • computational biology
  • multifurcating phylogenetic tree
  • maximum agreement forest
  • TBR distance
  • fixed-parameter algorithm
  • 012102

关键词

  • 计算生物学
  • 多叉系统发生树
  • 最大一致森林
  • TBR距离
  • 固定参数算法