# Age Optimal Information Gathering and Dissemination on Graphs

## TL;DR

This paper studies how to optimally schedule a mobile agent to exchange timely updates with ground terminals over a graph, minimizing age of information metrics, and proposes strategies with provable optimality bounds.

## Contribution

It introduces randomized and age-based trajectories for minimizing age of information, providing theoretical bounds and complexity results for these strategies.

## Key findings

- Randomized trajectories are peak age optimal and approximately average age optimal.
- Average age minimization is NP-hard.
- Age-based trajectory is within a factor of 2 of optimal in symmetric cases.

## Abstract

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 $P_{i,j}$. For the information gathering problem, we show that a randomized trajectory is peak age optimal and factor-$8\mathcal{H}$ average age optimal, where $\mathcal{H}$ 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-$O(\mathcal{H})$ 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.