Figure 2.

Example of suboptimal median. Let G(k)=7 + k. The center sequence is the median for the alignment of the left and right sequences. (The underscored C represents {C,indel}.) Although the upper and lower sequences are included in the median, the lower one is not in an optimal edit path connecting left and right. This example shows Lemma 2 does not hold for affine gap costs. Therefore, there are sequences in this RAG that cannot be used directly in the DO algorithm without an extra cost, not computed by e_P. It follows that DO, if used directly for the affine gap cost case, can compute an incorrect cost for a given tree.