Computing nonbinary agreement forests

Given two rooted phylogenetic trees, the Maximum Agreement Forest problem (MAF) asks to find a forest that is, in a certain sense, common to both trees and has a minimum number of components. There has been considerable interest in a special case of this problem, in which the input trees are required to be binary. This binary version of the problem has been shown to be 3-approximable in linear time and to be solvable exactly in O(2.42^k n) time, with k the number of components of a maximum agreement forest and n the number of leaves. The general, nonbinary problem is known to have a (d+1)-approximation for trees with outdegree at most d, and a kernel of size 64k. Here we show that nonbinary MAF has a polynomial-time 4-approximation and an (exact) fixed-parameter tractable algorithm that runs in O(4^k poly(n)) time. The algorithms have been implemented and are publicly available.

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