Fixed-Parameter and Approximation Algorithms for Maximum Agreement Forests of Multifurcating Trees

We present efficient algorithms for computing a maximum agreement forest (MAF) of a pair of multifurcating (nonbinary) rooted trees. Our algorithms match the running times of the currently best algorithms for the binary case. The size of an MAF corresponds to the subtree prune-and-regraft (SPR) distance of the two trees and is intimately connected to their hybridization number. These distance measures are essential tools for understanding reticulate evolution, such as lateral gene transfer, recombination, and hybridization. Multifurcating trees arise naturally as a result of statistical uncertainty in current tree construction methods.