Figure 3

DAG interpretation of the diploid to diploid alignment. Above, a DAG that represents the alignment (S^A, S^B), and below, a DAG that represents the alignment (S^X, S^Y), both from the example of Figure 1. From each DAG we extract two covering paths. That means that every node is visited by at least one path. An optimal solution to the synchronized diploid to diploid distance is given by the two paths extracted from the first DAG generating the sequences actggaaa and agggcca and the two paths from the second one generating the sequences atagaaa and agcggcca. The synchronized diploid to diploid distance is then d(actgaaa, ataaaa) + d(aggcca, agcgcca) = 2 + 1 = 3. Here the unit cost edit distance scores are used. Observe that the optimal diploid to diploid distance is 1 corresponding to the solution of pair of haploids to diploid alignment in Figure 1, and that is also possible to extract paths that represent the solution of the diploid to diploid distance.