Approximation Schemes for Age of Information Minimization in UAV Grid Patrols

TL;DR

This paper develops approximation schemes for UAV patrol routing to minimize the average Age of Information in grid systems, providing theoretical bounds and practical heuristics for complex environments.

Contribution

Introduces two polynomial-time approximation schemes with a ratio of 2 for AoI minimization in UAV patrols on general graphs, along with a heuristic for improved performance.

Findings

Approximation schemes achieve a ratio of 2.

Evenly distributing edge visits reduces AoI.

Heuristic maintains approximation ratio and performs well on random graphs.

Abstract

Motivated by the critical need for unmanned aerial vehicles (UAVs) to patrol grid systems in hazardous and dynamically changing environments, this study addresses a routing problem aimed at minimizing the time-average Age of Information (AoI) for edges in general graphs. We establish a lower bound for all feasible patrol policies and demonstrate that this bound is tight when the graph contains an Eulerian cycle. For graphs without Eulerian cycles, it becomes challenging to identify the optimal patrol strategy due to the extensive range of feasible options. Our analysis shows that restricting the strategy to periodic sequences still results in an exponentially large number of possible strategies. To address this complexity, we introduce two polynomial-time approximation schemes, each involving a two-step process: constructing multigraphs first and then embedding Eulerian cycles within these multigraphs. We prove that both schemes achieve an approximation ratio of 2. Further, both analytical and numerical results suggest that evenly and sparsely distributing edge visits within a periodic route significantly reduces the average AoI compared to strategies that merely minimize the route travel distance. Building on this insight, we propose a heuristic method that not only maintains the approximation ratio of 2 but also ensures robust performance across varying random graphs.