Shortest Path Induced Vertex Ordering and its Application to Multi-agent Formation Path Planning

For the task of moving a group of indistinguishable agents on a connected graph with unit edge length into an arbitrary goal formation, it was shown previously that distance optimal paths can be planned to complete with a tight convergence time guarantee. In this study, we show that the problem formulation in fact induces a more fundamental structure on the underlying graph network, which directly leads to an algorithm with similar performance characteristics. We then generalize the results to graphs with integer edge lengths and capacities.