The determination of the computational complexity of multi-agent pathfinding
on directed graphs has been an open problem for many years. For undirected
graphs, solvability can be decided in polynomial time, as has been shown
already in the eighties. Further, recently it has been shown that a special
case on directed graphs is solvable in polynomial time. In this paper, we show
that the problem is NP-hard in the general case. In addition, some upper bounds
are proven