DMVP: Foremost Waypoint Coverage of Time-Varying Graphs

We consider the Dynamic Map Visitation Problem (DMVP), in which a team of agents must visit a collection of critical locations as quickly as possible, in an environment that may change rapidly and unpredictably during the agents’ navigation. We apply recent formulations of time-varying graphs (TVGs) to DMVP, shedding new light on the computational hierarchy R ⊃ B ⊃ P of TVG classes by analyzing them in the context of graph navigation. We provide hardness results for all three classes, and for several restricted topologies, we show a separation between the classes by showing severe inapproximability in R, limited approximability in B, and tractability in P. We also give topologies in which DMVP in R is fixed parameter tractable, which may serve as a first step toward fully characterizing the features that make DMVP difficult.