An improved fixed-parameter algorithm for minimum-flip consensus trees

Abstract

In computational phylogenetics, the problem of constructing a consensus tree for a given set of input trees has frequently been addressed. In this paper we study the Minimum-Flip Problem: the input trees are transformed into a binary matrix, and we want to find a perfect phylogeny for this matrix using a minimum number of flips, that is, corrections of single entries in the matrix. In its graph-theoretical formulation, the problem is as follows: Given a bipartite graph G = (Vt∪∈V c, E), the problem is to find a minimum set of edge modifications such that the resulting graph has no induced path with four edges which starts and ends in Vt . We present a fixed-parameter algorithm for the Minimum-Flip Problem with running time O(4.83 k (m + n) + n) for n taxa, m characters, and k flips. Additionally, we discuss several heuristic improvements. We also report computational results on phylogenetic data. © 2008 Springer-Verlag Berlin Heidelberg.