Abstract
In computational phylogenetics, the problem of constructinga consensus tree for a given set of input trees has frequently been addressed.In this paper we study the Minimum-Flip Problem: the inputtrees are transformed into a binary matrix, and we want to find a perfectphylogeny 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∪Vc, E),the problem is to find a minimum set of edge modifications such that theresulting graph has no induced path with four edges which starts andends in Vt. We present a fixed-parameter algorithm for the Minimum-Flip Problemwith running time O(4.83k (m+n)+mn) for n taxa, m characters,and k flips. Additionally, we discuss several heuristic improvements. Wealso report computational results on phylogenetic data.
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