On Optimal Coverage with Unreliable Sensors*

This paper regards the problem of placing unreliable sensors in a given one-dimensional environment, in such a way to optimize a given coverage cost. We specifically consider the disk-coverage cost, whose optimal solution for reliable sensors is simply an equally-spaced configuration of the sensors. If we allow that the sensors may fail to take or communicate their measurements, this solution may instead not be optimal. However, as the number of sensors grows to infinity, the ratio between the cost of equally-spaced configurations and the optimal failure-free cost only grows as the logarithm of the number of sensors. We interpret this result as a confirmation of the intrinsic robustness of sensor networks.