"How sure are you that the converse is not also true? Will you at least admit this is an interesting question? Or even the question of how to ask this question

"How sure are you that the converse is not also true? Will you at least admit this is an interesting question? Or even the question of how to ask this question in such a way that it is provable/disprovable. I think this is worthwile." It's an interesting question, but one which has a sad answer: integer linear programming (and other restricted forms, such as 0-1 programming) are NP-Hard. If you could use dijkstra's algorithm to solve them, in less than exponential time, you will have proved P=NP. So i would go with "pretty sure". (now, could you do it in exponential number of dijkstra invocations? Maybe? But that is, to me, not an interesting question :P Same with could you expand the linear programming problem into an exponential size graph that was then solvable by dijkstra's algorithm - we already know that expspace is a superset of p, etc)