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

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(4 k n 5 ) for the problem.

An improved FPT algorithm for the flip distance problem

“…A parameterized problem is a decision problem for which every instance is of the form (x, k), where x is the input instance and k ∈ N is the parameter. A parameterized problem is fixed-parameter tractable (FPT ) if it can be solved by an algorithm (FPT algorithm) in O(f (k)|x| O (1) ) time, where f (k) is a computable function of k. In addition to computational geometry, parameterized problems in other areas such as graph theory [8,9,12], computational biology [3,22] and MAX-SAT [6] are also studied extensively. For a further introduction to parameterized algorithms, readers could refer to [4,7].…”

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

“…Whidden et al [22] presented an algorithm of running time O(2.42 k k + n 3 ) for the soft version of the Maximum Agreement Forest problem on two rooted multifurcating phylogenetic trees. Shi et al [39] presented an algorithm of running time O(4 k n 5 ) for the hard version of the Maximum Agreement Forest problem on two unrooted multifurcating phylogenetic trees. Chen et al [23] developed an improved algorithm of running time O(3 k n), which is the best known result for the hard version of the Maximum Agreement Forest problem on two unrooted multifurcating phylogenetic trees.…”