A 1/2-Approximation Algorithm for Target Coverage Problem in Mobile Air Quality Monitoring Systems

Viet-Dung Nguyen, Phi-Le Nguyen, Trung Hieu Nguyen, Phan-Thuan Do

Abstract: So far, air quality monitoring is usually handled by monitoring stations located at fixed locations. However, due to the cost of installation, deployment, and operation, the number of monitoring stations deployed is often tiny; thus, the monitored area is limited. To deal with this problem, in this paper, we consider a mobile air quality monitoring system that relies on sensors mounted on buses to broaden the monitoring area. Specifically, we investigate the optimal buses to place the sensors as well as the optimal monitoring timings to maximize the number of critical regions that are monitored. We mathematically formulate the targeted problem and prove its NP-hardness. Then, we exploit the greedy and dynamic programming approaches to propose a polynomial-time 1/2-approximation algorithm. We use the data of real bus routes in Hanoi, Vietnam, for the experimentation and show that the proposed algorithm guarantees an average performance ratio of 72.68%.