EDIT: Preliminary results 1
In case there are people who are interested.Finally found some time to do some coding.Implemented branching cutting via symmetry.
The third column can be viewed as a simple backtracking algorithm but with first 4 vertices fixed. (Therefore symbolizing full path search)
This result seems to show that 2
I should expect the simple symmetry had written better pruning codes and I realized that it takes only at most a couple of paths method weeks to be about 4 times improvement over backtracking (consistently 4 times smaller)finish the running.Simply putHowever, it is not much based on extrapolation of an improvement.
The unoptimized run time for path length 19 is about 400 seconds, which seems to multiply by about 2.5 per increment, where the number of unique paths also multiply by around that amount. This factor initial few branches I had completed, I will slowly decrease as the path length increase.
Around fixing need some whooping 5+ TB of 30 or so vertices, it becomes instantaneous hard disk space just to check store the remaining pathsresults.By some naive estimate Comparing with just measly 24 Hamiltonian cycles for $n=5$, it seems pretty clear that even if I can now try to brute force this in a few months..find all cycles for $n=9$ there is no way I can store all of them. Sad =(