The three possible ways to handle leaf ci, depending on whether we satisfy clause Ci with its first, second or third literal, respectively corresponding to j = 1, j = 2 and j = 3. The colors on the nodes are there to emphasize which node receives ci as a child after the cherry reduction sequence.
In phylogenetic networks, picking a cherry consists of removing a leaf that shares a parent with another leaf, or removing a reticulate edge whose endpoints are parents of leaves. Cherry-picking operations were recently shown to have several structural and algorithmic applications in the study of networks, for instance in determining their reconstr...
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... there are multiple choices for j, choose one arbitrarily. Depending on j, apply one of the cherry sequences appearing in Figure 8. The figure assumes a clause C i with three literals. ...
Phylogenetic networks are increasingly being considered as better suited to represent the complexity of the evolutionary relationships between species. One class of phylogenetic networks that has received a lot of attention recently is the class of orchard networks, which is composed of networks that can be reduced to a single leaf using cherry reductions. Cherry reductions, also called cherry-picking operations, remove either a leaf of a simple cherry (sibling leaves sharing a parent) or a reticulate edge of a reticulate cherry (two leaves whose parents are connected by a reticulate edge). In this paper, we present a fixed-parameter tractable algorithm to solve the problem of finding a maximum agreement cherry-reduced subnetwork (MACRS) between two rooted binary level-1 networks. This is the first exact algorithm proposed to solve the MACRS problem. As proven in earlier work, there is a direct relationship between finding an MACRS and calculating a distance based on cherry operations. As a result, the proposed algorithm also provides a distance that can be used for the comparison of level-1 networks.Supplementary material for this paper can be found on arXiv.org.KeywordsCherry operationsGraphs and networksTreesNetwork problemsAlgorithm design and analysisBiology and geneticsPhylogenetic Networks