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



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.


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


  • 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