Is this covering problem NP-hard? Given a rectangular region $R$ and a set $D$ of $n$ disks such that the union of all disks in $D$ cover the entire rectangular region $R$, the objective is to find the minimum cardinality set $D'$ subset of $D$ such that the union of all disks in $D'$ cover the entire $R$.
I believe that this problem is NP-hard, but did not find any reference. can somebody help me to find the one or reduction from an NP-hard problem.
If I arrange the disks into a spiral pattern then the problem is NP-hard. It may be even harder in your general case. This would be a variation on the polygon covering problem.

See https://en.wikipedia.org/wiki/Polygon_covering