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Fig. 3 | BMC Genomics

Fig. 3

From: Genomic duplication problems for unrooted gene trees

Fig. 3

An example of unrooted episode clustering. A species tree S and four unrooted gene trees G 1, G 2, G 3, G 4 with all D-minimal rootings. For every gene tree two star topologies are shown: one for the duplication-loss cost (left) and one for the duplications cost (right). Every edge of a gene tree is decorated with the corresponding cost of rooting. Every duplication node in rootings of gene trees is decorated by all possible locations (i.e., valid mappings) of its duplication cluster from optimal solutions of single-UEC. Note that the rooting G 4, whose lca-mappings are shown in Fig. 1, has two duplications at (c,(b,a)) and (h,(f,g)) that are raised (here) to create two duplications clusters. Let {G 2,G 4} be an instance of UEC Problem. Then, the -cluster, that is present in G 2, contributes to the optimal solution. In such a case, the solution is induced by one of the two instances of EC problem: {G 2,G 4,1} or {G 2,G 4,7}. This property is proved in Theorem 5 and in Lemma 6

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