Fig. 3

An example of the procedure for assigning nucleotide codes to the ‘start and end’ vertices of the connected component shown in Fig. 2. In this example, position 21 is selected as a root vertex v _arb. Then we consider the tree structure for assigning nucleotides to the ‘start and end’ vertices, where the order of the ‘start and end’ vertices is obtained by the depth-first search in the spanning tree of the connected component (in this example, the order of positions 21, 25, 37, and 42 from the top to the bottom of the tree). Dashed arrows mean that there exists a decomposed path between two positions. In this example, first, an A or G is randomly selected for position 21 (it is noted that, in the case of the nucleotide assignment for the GA initialization, not an A or G, but an A, C, G or U is randomly selected here). Then nucleotide codes of the remaining positions are assigned from the top of the tree to the bottom. Let us consider an A is selected for position 21. Even in the case such that a C alone is allowed to position 37 due to a sequence constraint, first we try to assign AUU from the top to the bottom; however, since this violates the constraint, we backtrack to position 25 and then assign a C to position 37. As a result, we assign AUCA to the ‘start and end’ vertices in this example