Figure 4

An illustration of the computation of Equation7. (a) The instance$\left(T_u^v,S_{u^{\prime }}^{v^{\prime }}\right)$ in the left-hand side of the equation. (b) The computation of term I in the right-hand side of the equation: The term considers the best alignment score under the assumption that u is smoothed. In this case, the score is obtained by taking the smoothing cost of u, and summing it, for some x ∈ N(u) ∖ {v}, with the alignment score between$T_x^u$ and$S_{u^{\prime }}^{v^{\prime }}$ and the pruning cost of all subtrees$T_y^u$ for y ∈ N(u)∖{v,x}. Vertex x is chosen to be the neighbor of u that induces a minimum cost with respect to this computation. The computation of term II is symmetric. (c) The computation of term III in the right-hand side of the equation: This term considers the case were neither u nor u′ are smoothed, and therefore these two nodes are aligned to each other. In this case, the score is computed similarly to the computation in Equation 5, with respect to the sets N(u) ∖ {v} and N(u′)∖{v′}.