I have a weighted digraph graph $G = (V,E)$ where the weights are positive and negative integers. The graph $G$ is not necessarily acyclic.
The question is: given 2 nodes $v_1$ and $v_2$, is there a path from $v_1$ to $v_2$ with a weight $w$.
I would like to know if there are any known complexity results for this problem, or even anything related to this but with a specific weight, and not just shortest path, longest path etc. I have been thinking of representing the problem as in-equations in some type of linear programming, but before I start I'd like to get as much info as possible :)