  For the task of moving a set of indistinguishable agents on a connected graph
with unit edge distance to an arbitrary set of goal vertices, free of
collisions, we propose a fast distance optimal control algorithm that guides
the agents into the desired formation. Moreover, we show that the algorithm
also provides a tight convergence time guarantee (time optimality and distance
optimality cannot be simultaneously satisfied). Our generic graph formulation
allows the algorithm to be applied to scenarios such as grids with holes
(modeling obstacles) in arbitrary dimensions. Simulations, available online,
confirm our theoretical developments.
