On the Elusiveness of Clusters
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Computing the rooted triplet distance between galled trees by counting triangles
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
On the complexity of computing the temporal hybridization number for two phylogenies
Discrete Applied Mathematics
Computing the rooted triplet distance between galled trees by counting triangles
Journal of Discrete Algorithms
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A phylogenetic network is a directed acyclic graph that visualizes an evolutionary history containing so-called reticulations such as recombinations, hybridizations or lateral gene transfers. Here we consider the construction of a simplest possible phylogenetic network consistent with an input set T, where T contains at least one phylogenetic tree on three leaves (a triplet) for each combination of three taxa. To quantify the complexity of a network we consider both the total number of reticulations and the number of reticulations per biconnected component, called the level of the network. We give polynomial-time algorithms for constructing a level-1 respectively a level-2 network that contains a minimum number of reticulations and is consistent with T (if such a network exists). In addition, we show that if T is precisely equal to the set of triplets consistent with some network, then we can construct such a network with smallest possible level in time O(|T|k+1), if k is a fixed upper bound on the level of the network.