I have a collections of map points (about 500 thousand, on an UTM grid if it matters), each of which has a non-negative weight, and I would like to find the circle with some fixed radius r that contains the largest total weight of points. An obvious first approximation to the problem is to buffer every point to the appropriate radius, find all points contained in that circle and sum their weights and returning the maximum; but it's also easy to construct instances where this approach fails to find the optimal solution.
So I'm wondering if this is a problem that can be tractably solved to find the optimal circle? My gut feeling is that it's probably intractable, but my geometry skills aren't good enough to make much headway in any direction. But it also feels like the kind of problem that already has a name and an accepted answer, I just don't know how to find it.
