  This paper studies a team coordination problem in a graph environment.
Specifically, we incorporate "support" action which an agent can take to reduce
the cost for its teammate to traverse some edges that have higher costs
otherwise. Due to this added feature, the graph traversal is no longer a
standard multi-agent path planning problem. To solve this new problem, we
propose a novel formulation by posing it as a planning problem in the joint
state space: the joint state graph (JSG). Since the edges of JSG implicitly
incorporate the support actions taken by the agents, we are able to now
optimize the joint actions by solving a standard single-agent path planning
problem in JSG. One main drawback of this approach is the curse of
dimensionality in both the number of agents and the size of the graph. To
improve scalability in graph size, we further propose a hierarchical
decomposition method to perform path planning in two levels. We provide
complexity analysis as well as a statistical analysis to demonstrate the
efficiency of our algorithm.
