Multi-agent Path Planning and Network Flow
This provides a theoretical framework for efficient multi-agent path planning, applicable in robotics and logistics, but is incremental as it builds on existing network flow methods.
The paper tackles multi-agent path planning on graphs by reducing it to network flow problems, enabling the use of combinatorial algorithms and linear programming, and proves a worst-case bound of n + V - 1 steps for permutation-invariant goals with an O(nVE) time algorithm.
This paper connects multi-agent path planning on graphs (roadmaps) to network flow problems, showing that the former can be reduced to the latter, therefore enabling the application of combinatorial network flow algorithms, as well as general linear program techniques, to multi-agent path planning problems on graphs. Exploiting this connection, we show that when the goals are permutation invariant, the problem always has a feasible solution path set with a longest finish time of no more than $n + V - 1$ steps, in which $n$ is the number of agents and $V$ is the number of vertices of the underlying graph. We then give a complete algorithm that finds such a solution in $O(nVE)$ time, with $E$ being the number of edges of the graph. Taking a further step, we study time and distance optimality of the feasible solutions, show that they have a pairwise Pareto optimal structure, and again provide efficient algorithms for optimizing two of these practical objectives.