I am interested in the following problem: in $\mathbb{R}^n$, we have $N$ overlapping hyperspheres all with the same radius. Given a point $p$ in $\mathbb{R}^n$, the objective is to find the $K$ hyperspheres whose centers are the closest to $p$ under the Euclidean metric (although I'm eventually interested in exploring other metrics as well). However, these hyperspheres cannot overlap with each other.

I know this can be formulated as maximum weighted independent set (with a cardinality constraint) in a geometric graph, where the weights are the distance from $p$, and we have an adjacency matrix which reflects whether the distance between two hypersphere centers is less than some constant, but I'm not sure if there is some other formulation I am missing.

I am also considering this from a probabilistic perspective, in the case where we can assume that the hyperspheres are uniformly distributed.