Multi-agent Path Planning and Network Flow

Details Multi-agent Path Planning and Network Flow Multi-agent Path Planning and Network Flow

2012-04-25

arxiv.org/abs/1204.5717v2

Computer Science

Data Structures and Algorithms

Somehow, the paper was listed with the wrong primary category (cs.DS), possibly due to some browser bug in the submission proc

Scientific paper

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 each of these practical objectives.

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