I am studying for an algorithms exam and ran into this example problem.
A circular disk with radius $2r$ can be covered by $7$ circular disks with radius $r$; in the following you can use this statement without proof.
Suppose that we are given a set $S$ of $n$ points in the plane, and we want to cover all points in $S$ by a minimum number of circular disks of radius $1$. Let $k$ be the optimal number of disks needed. Propose a polynomial time algorithm to produce a covering with at most $7k$ circular disks of radius $1$.
I do understand the question but I have no idea where to begin or how to approach this. Should a reduction be used? Or is there a simple and obvious answer? How do you cover $n$ points that you know nothing about? Maybe calculate the distances between them?
I do realize that if the distance between all points is greater than $2$ units, then $k = n$ since every circle of radius $2$ can only cover a single point.
I mainly want to understand the problem so that I can attempt a solution on my own, but a solution to the problem would also be nice, so that I can check my answer later.