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 N 1,N 2 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 N 1 and N 2. 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(n m/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.
KeywordsCharacteristic Vector Internal Node Faster Computation Outer Face Phylogenetic Network
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