Fig. 2
From: Efficient gene orthology inference via large-scale rearrangements
On the top part we show the capping of the decomposition corresponding to the (black) ortholog-set \({\mathcal {O}}=\{\{\texttt{1},\texttt{7}\}\), \(\{\texttt{3},\texttt{10}\}, \{\texttt{4},\texttt{9}\}, \{\texttt{5},\texttt{13}\}\}\) from the gene similarity graph \(\mathcal {S}({\mathbb {A}},{\mathbb {B}})\) of Fig. 1 (bottom). Each red vertex is a cap vertex. Each filled (red) vertex is connected to a telomere (chromosome/path ends). The unfilled vertices represent the extra (equalizing) vertices connected by a dummy adjacency. The capping is a perfect matching of the complete bipartite graph of the cap vertices. The optimal capping for this decomposition is highlighted. It closes each of its paths into a separate cycle. (In general, an optimal capping of a decomposition may link up to 4 paths into a single cycle [8]). On the bottom part is displayed the complete family-free graph \(F\!F\!R({\mathbb {A}},{\mathbb {B}},\mathcal {S})\) optimally capped. Cap edges are unweighted. Scores of extremity edges and weights of indel edges are omitted