I'm trying to solve an interesting problem. Imagine a square surface, onto which we spray randomly p points. We also (randomly) place c circle centres. I'm trying to find an algorithm that will allow me to find the radii for the circles that cover as many points as possible, subject to the constraints that:

-the radii are bounded (maximum radius r_max)

-circles cannot intersect/overlap.

My approach so far was to compute a rank 3 tensor. Start from a definition: a point is denied by a circle, if the circle, by taking another point, causes that the point cannot be covered by any of the remaining circles without violating the constraints. The size of tha tensor is C x P x P, where C - number of circles, P - number of points. I initialize it with zeros. I then check whether if circle c takes point p, point p' is denied, which I signify in the tensor by setting the appropriate value to 1. From this data I'm trying to deduce whether it's worth trying to encircle a point, e.g. if a point is denied by many points, it probably means that it's a distant, isolated point, or that denying point form a cluster. I didn't manage to find a way that would allow me to make general any statements though.

Any ideas how to extend my approach / any suggestions to do it differently would be most welcome!

I'm trying to solve an interesting problem. Imagine a square surface, onto which we spray randomly $p$ points. We also (randomly) place $c$ circle centres. I'm trying to find an algorithm that will allow me to find the radii for the circles that cover as many points as possible, subject to the constraints that:

• the radii are bounded (maximum radius $r_{max}$)
• circles cannot intersect/overlap.

My approach so far was to compute a rank 3 tensor. Start from a definition: a point is denied by a circle, if the circle, by taking another point, causes that the point cannot be covered by any of the remaining circles without violating the constraints. The size of tha tensor is $C \times P \times P$, where $C$ is the number of circles, and $P$ is the number of points. I initialize it with zeros. I then check whether if circle c takes point p, point p' is denied, which I signify in the tensor by setting the appropriate value to 1. From this data I'm trying to deduce whether it's worth trying to encircle a point, e.g. if a point is denied by many points, it probably means that it's a distant, isolated point, or that denying point form a cluster. I didn't manage to find a way that would allow me to make general any statements though.

Any ideas how to extend my approach / any suggestions to do it differently would be most welcome!