Figure 7

Examples of component trees. (i) The tree T ( A , B ) for the relational diagram represented in Figure 2 has one bad (white) and three good (black) nodes, and (ii) the corresponding colored tree T _o ( A, B ). Here, the indel-type of each cycle is given. In both cases the trees $T^{\prime }$ and $T_o^{\prime }$ are composed of a single bad node. (iii) An example of a $T_o^{\prime }$ to show that a greedy strategy, of maximizing the merging of leaves with the same colored dot, does not work. If we merge the two leaves with blue dots the cost of the cover is 5. However, if we merge twice a leaf with a blue dot and a leaf with no dot (the longer paths), the cost is 4. (iv) Another example of a $T_o^{\prime }$ to show that, on the other hand, if we merge the leaves of the longer path we have a cost of 3. But if instead we merge the two nodes with blue dots and the two nodes with orange dots, the cost is 2.