I had a problem with this too. But actually the problem can be stated as an NP problem: Compute a round-trip shorter than k. If you have an algorithm to solve t

I had a problem with this too. But actually the problem can be stated as an NP problem: Compute a round-trip shorter than k. If you have an algorithm to solve the NP version then you can use it to find the shortest round-trip by repeadly applying it to different k-parameters.