  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.
