Assume I have a euclidean TSP solver that is optimal, but it can only solve inputs with exactly $N$ vertices. Let's call it the N-solver.
Now, I have an input with $K$ vertices in the 2D plane, where $K < N$. Can I convert this $K$ sized input to an $N$ sized input where I can feed it into my N-solver and obtain an optimal answer, and then try to convert it back to an optimal solution for the original $K$ vertices?
I assume that you are not allowed to have multiple vertices at the same coordinate.
Has this problem been discussed, investigated, or solved anywhere? Even some approach that guarantees some gap compared to the optimal answer would be good. Any thoughts?