Figure 8

Solving the Guided Intermediate problem for BP( A , B ) with two AB-cycles, and guide G = { pq , rs , uv }. At each step, an adjacency from G is taken, and if accepted its vertices and incident edges are removed, and two new edges are added to complete the resulting two smaller AB-cycles. The problem is then recursively solved on the smaller cycles. (a) Initial BP(A, B), where adjacency pq is accepted. (b) Second adjacency rs is also accepted. (c) The adjacency uv covers two components, because it crosses with a previously added adjacency, and it is rejected. (d) In the end of the algorithm, three extra adjacencies (shown as dotted orange edges) are added for each AB-cycle of size 2, since this is the only choice for a non-crossing edge belonging to an intermediate genome M. The final output is then the adjacency set {pq, rs} plus the three adjacencies corresponding to the dotted orange edges.