The path algorithm looks much easier to me.

I would personally be inclined to use the standard breadth-first shortest-path algorithm, with a heuristic saying that there is no need to fill in information about the shortest path outside of some distance from the shortest-line path.

No need to bring in knot theory. Besides which, knot theory is interesting because we don't understand it well. For computer algorithms it is better to work with things that we understand. :-)

Anyways I won't be trying that. I tried the tour and circuit because they looked like much harder (and therefore more interesting) problems.

Cheers,
Ben