Dynamic Connected Cooperative Coverage Problem

We study the so-called dynamic coverage problem by agents located in some topological graph. The agents must visit all regions of interest but they also should stay connected to the base via multi-hop. We prove that the algorithmic complexity of this planning problem is PSPACE-complete. Furthermore we prove that the problem becomes NP-complete for bounded plans. We also prove the same complexities for the reachability problem of some positions. We also prove that complexities are maintained for a subclass of topological graphs.