A parameterized algorithm for the Maximum Agreement Forest problem on multiple rooted multifurcating trees

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 parameterized algorithms. By taking advantage of a new branch-and-bound strategy, a parameterized algorithm with running time O(2.42km3n4) is presented for the problem, assuming that all polytomies in the multifurcating phylogenetic trees are hard.