Maximum-coverage minimum-overlap intersection of sets
Without knowing anything about the restrictions to your problem, the general version is Set cover, one of Karp's 21 NP-complete problems.
However, if you know more about the structure of the data, you might be able to get better algorithms, see for example the Art gallery problem, where you are given a polygon, and want to find the minimum number of guards/cameras you should place that cover the entire polygon.