Fixed-Parameter Algorithms for Maximum Agreement Forests

Fixed-Parameter and Approximation Algorithms for Maximum Agreement Forests

We present new and improved approximation and FPT algorithms for computing rooted and unrooted maximum agreement forests (MAFs) of pairs of phylogenetic trees. Their sizes correspond to the subtree-prune-and-regraft distances and the tree-bisection-and-reconnection distances of the trees, respectively. We also provide the first bounded search tree FPT algorithm for computing rooted maximum acyc...

Fixed-Parameter Algorithms for Finding Agreement Supertrees

Fixed Parameter Polynomial Time Algorithms for Maximum Agreement and Compatible Supertrees

Consider a set of labels L and a set of trees T = {T , T , . . . , T } where each tree T (i) is distinctly leaf-labeled by some subset of L. One fundamental problem is to find the biggest tree (denoted as supertree) to represent T which minimizes the disagreements with the trees in T under certain criteria. This problem finds applications in phylogenetics, database, and data mining. In this pap...

Approximation Algorithms for Nonbinary Agreement Forests

Given two rooted phylogenetic trees on the same set of taxa X, 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. The Maximum Acyclic Agreement Forest problem (MAAF) has the additional restriction that the components of the forest cannot have conflicting ancestral relations in the input trees...

Fixed-Parameter Tractability of the Maximum Agreement Supertree Problem extended abstract

Given a ground set L of labels and a collection of trees whose leaves are bijectively labelled by some elements of L, the Maximum Agreement Supertree problem (SMAST) is the following: find a tree T on a largest label set L ⊆ L that homeomorphically contains every input tree restricted to L. The problem finds applications in several fields, e.g. phylogenetics. In this paper we focus on the param...