Fig. 1
From: Approximating the correction of weighted and unweighted orthology and paralogy relations
S is the species tree for \(\Sigma = \{a,b,c,d\}\). The internal nodes, representing ancestral species, are labeled by x, y and z. R is a relation graph on gene set \({\Gamma }= \{a_1, a_2, b_1, c_1, d_1\}\). A gene name corresponds to the species it belongs to (e.g. \(s(a_1) = a\)). R is not satisfiable as the set of vertices \(\{c_1, b_1, d_1, a_2\}\) induces a \(P_4\). \(R'\) is a satisfiable relation graph obtained from R by inserting the edge \(\{c_1,d_1\}\), and \(G_1\) is a DS-tree displaying every relation of \(R'\) (each internal node v is labeled by \(s_{G_1}(v)\)). However, \(G_1\) is not consistent with the species tree S. \(R''\) is another correction of R that is S-consistent, as the tree \(G_2\) displays the relations in \(R''\) and is S-consistent. Dup nodes in DS-trees are marked by a square; all other nodes are speciation nodes