多根多叉树最大一致森林问题的参数化算法
Parameterized Algorithms for the Maximum Agreement Forest Problem on Multiple Rooted Multifurcating Trees
摘要：
最大一致森林问题在遗传学中得到了广泛的研究。大多数以前的工作是在两个二元系统发育树。在本文中，我们研究了一个广义版本的问题：最大协议森林问题的多根多叉系统发生树，从固定参数算法的角度。通过利用一个新的分支定界策略，两个参数化的算法，与运行时间$O(2.42^k m^3 n^4)$和$O(2.74^k m^3 n^5)$，分别为硬版本和软版本的问题，这对应于两个不同的生物学意义的多分支系统发育树。
英文摘要：
The Maximum Agreement Forest problem has been extensively studied in phylogenetics. Most previous work is on two binary phylogenetic trees. In this paper, we study a generalized version of the problem: the Maximum Agreement Forest problem on multiple rooted multifurcating phylogenetic trees, from the perspective of fixed-parameter algorithms. By taking advantage of a new branch-and-bound strategy, two parameterized algorithms, with running times $O(2.42^k m^3 n^4)$ and $O(2.74^k m^3 n^5)$, respectively, are presented for the hard version and the soft version of the problem, which correspond to two different biological meanings to the polytomies in multifurcating phylogenetic trees.
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