So, if I were using a black-box decision algorithm,
PATH in which I could say, "does a path of weight
k exist in this graph from
V", problably the typical way one would solve the optimization problem of shortest path is to start at
k at zero and increment until
PATH returns true. But since paths start at
-inf shouldn't we be starting there? (Thus making this optimization problem not solvable in polynomial time)
I know this isn't right, I'm just having a hard time seeing which part I am missing here.