The Valeriepieris Circle is a circle within which it is supposed that the majority of the World's population lives. I'm interested in general-case and average-case algorithms for finding such a circle.
I'm aware that this can be done in $O(nm)$ and perhaps $O(n + m)$ where $n $ is the number of pixels and $m$ is the number of circle sizes, given data is discrete. While finding such a solution is of interest for practical reasons, I'm also interested in algorithms for the continuous case.
Generalization
A more generalized form of the problem at hand might be something like...
Given an n-dimensional manifold over which a variable $X$ is distributed, find the smallest n-sphere satisfying the constraint $\Gamma$.
The most interesting average case is the original (human population over a globe):
- Clustering; perhaps we can optimize for a Hopkins stat $H > 0.5$.
- Just a regular old Euclidean manifold suffices.
