Improved Fixed-Parameter Algorithms for Minimum-Flip Consensus Trees

Abstract

In computational phylogenetics, the problem of constructing a consensus tree for a given set of rooted input trees has frequently been addressed. In this article 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. The graph-theoretical formulation of the problem is as follows: Given a bipartite graph G = ( Vt ∪ Vc , E ), the task is to find a minimum set of edge modifications such that the resulting graph has no induced path with four edges that starts and ends in Vt , where Vt corresponds to the taxa set and Vc corresponds to the character set. We present two fixed-parameter algorithms for the Minimum-Flip Problem , one with running time O (4.83 k + poly ( m , n )) and another one with running time O (4.42 k + poly ( m , n )) for n taxa, m characters, k flips, and poly ( m , n ) denotes a polynomial function in m and n . Additionally, we discuss several heuristic improvements. We also report computational results on phylogenetic data.