We consider the problem of timely exchange of updates between a central
station and a set of ground terminals V, via a mobile agent that traverses
across the ground terminals along a mobility graph G=(V,E). We design the
trajectory of the mobile agent to minimize peak and average age of information
(AoI), two newly proposed metrics for measuring timeliness of information. We
consider randomized trajectories, in which the mobile agent travels from
terminal i to terminal j with probability Pi,j​. For the information
gathering problem, we show that a randomized trajectory is peak age optimal and
factor-8H average age optimal, where H is the mixing
time of the randomized trajectory on the mobility graph G. We also show that
the average age minimization problem is NP-hard. For the information
dissemination problem, we prove that the same randomized trajectory is
factor-O(H) peak and average age optimal. Moreover, we propose an
age-based trajectory, which utilizes information about current age at
terminals, and show that it is factor-2 average age optimal in a symmetric
setting