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 = (V t ∪ 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 V t .
We present a fixed-parameter algorithm for the Minimum-Flip Problem with running time O(4.83k (m + n) + mn) for n taxa, m characters, and k flips. Additionally, we discuss several heuristic improvements. We also report computational results on phylogenetic data.
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Böcker, S., Bui, Q.B.A., Truss, A. (2008). An Improved Fixed-Parameter Algorithm for Minimum-Flip Consensus Trees. In: Grohe, M., Niedermeier, R. (eds) Parameterized and Exact Computation. IWPEC 2008. Lecture Notes in Computer Science, vol 5018. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79723-4_6
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DOI: https://doi.org/10.1007/978-3-540-79723-4_6
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