Faster Computation of the Robinson-Foulds Distance between Phylogenetic Networks
The Robinson-Foulds distance, which is the most widely used metric for comparing phylogenetic trees, has recently been generalized to phylogenetic networks. Given two networks N1,N2 with n leaves, m nodes, and e edges, the Robinson-Foulds distance measures the number of clusters of descendant leaves that are not shared by N1 and N2. The fastest known algorithm for computing the Robinson-Foulds distance between those networks runs in O(m(m + e)) time. In this paper, we improve the time complexity to O(n(m + e)/logn) for general networks and O(nm/logn) for general networks with bounded degree, and to optimal O(m + e) time for planar phylogenetic networks and bounded-level phylogenetic networks. We also introduce the natural concept of the minimum spread of a phylogenetic network and show how the running time of our new algorithm depends on this parameter. As an example, we prove that the minimum spread of a level-k phylogenetic network is at most k + 1, which implies that for two level-k phylogenetic networks, our algorithm runs in O((k + 1)(m + e)) time.
Unable to display preview. Download preview PDF.
- 3.Cardona, G., Llabrés, M., Rosselló, F., Valiente, G.: Metrics for phylogenetic networks I: Generalizations of the Robinson-Foulds metric. IEEE ACM T. Comput. Biol. 6(1), 1–16 (2009)Google Scholar
- 4.Cardona, G., Rosselló, F., Valiente, G.: Comparison of tree-child phylogenetic networks. IEEE ACM T. Comput. Biol. (2009)Google Scholar
- 10.Gusfield, D., Eddhu, S., Langley, C.: Efficient reconstruction of phylogenetic networks with constrained recombination. In: Proc. 2nd IEEE Computer Society Bioinformatics Conf., pp. 363–374 (2003)Google Scholar
- 19.Strimmer, K., Moulton, V.: Likelihood analysis of phylogenetic networks using directed graphical models. Mol. Biol. Evol. 17(6), 875–881 (2000)Google Scholar
- 20.Strimmer, K., Wiuf, C., Moulton, V.: Recombination analysis using directed graphical models. Mol. Biol. Evol. 18(1), 97–99 (2001)Google Scholar