An important problem in the study of sensor networks is how to select a set of sensors that maximizes coverage of other sensors. Given pair wise coverage values, three commonly found functions give some estimate of the aggregate coverage possible by a set of sensors: maximum coverage by any selected sensor (MAX), total coverage by all selected sensors (SUM), and the probability of correct prediction by at least one sensor (PROB). MAX and SUM are two extremes of possible coverage, while PROB, based on an independence assumption, is in the middle.
This paper addresses the following question: what guarantees can be made of coverage that is evaluated by an unknown sub-modular function of coverage when sensors are selected according to MAX, SUM, or PROB? We prove that the guarantees are very bad: In the worst case, coverage differs by a factor of sqrt(n), where n is the number of sensors. We show in simulations on synthetic and real data that the differences can be quite high as well. We show how to potentially address this problem using a hybrid of the coverage functions.