Figure 4

Example of how Max-Cut can be applied to the MinPreSpeDup problem. S is a species tree, $\mathcal{G}=\left\{G_1,G_2,G_3\right\}$ and $\mathcal{T}$ is the BUILD graph (solid edges). Its connected components are enclosed in circles, and the dotted edges represent required duplications mapped to r(S). The edge of weight 2 is explained by the a₁d₁|c₁ and d₁b₁|e₁ triplets, whereas the edge of weight 1 is explained by the c₁e₁|f₁ triplet. A Max-Cut creates the bipartition ({a₁, b₁, d₁, f₁}, {c₁, e₁}), leading to the T₁ tree which merges all required duplications at its root. The tree T₂ is obtained from the suboptimal bipartition ({a₁, b₁, d₁}, {c₁, e₁, f₁}) and has 2 duplications.