Minimum Target Coverage for Air Quality Monitoring Using Bus Routes

Several works recently focus on monitoring air quality of critical areas using sensors attached to buses. They aim to monitor the maximum number of critical areas using a limited number of sensors. In practice, we may want to have information for all critical areas. We work on the problem of covering all the areas using the minimum number of sensors in this work. We show that, even when the bus routes are not pre-defined, the problem is log-APX-hard and is significantly harder than the problem of the previous works. We develop two algorithms for the case that the routes are pre-defined. Those algorithms include a fixed parameter tractability and a greedy algorithm. Next, we show an NP-completeness reduction for a special case of the problem and propose a 2-approximation algorithm for it. Our experiment results show that, although we usually give the similar number of sensors as the algorithm in the previous works, our algorithms have a shorter computation time than the classical greedy algorithm.