Yes, there is no 1800-2000 link, but, if I understood the OP correctly, there is an overlapping path (1000-2000) so that the 1800-2000 itinary can be done through this path.

I was first thinking of a simple (possibly recursive) tree-walking algorithm, but given the possibility of crossing the 1800-2000 gap using the 1000-2000 link, the right solution is probably quite different.