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While preparing for final exam, I encountered a (target) problem where you have $M$ lines and $L$ points and you want to answer if it's possible to cover them all using $K$ disks of unit radius (decision problem).

I would like to reduce the Disk Covering Problem to the problem at hand to show that the problem is NP-hard. Is my logic valid if I construct an instance of the target problem with no lines, meaning to set $M=0$, and reduce an arbitrary instance of the disk covering problem to it? or does setting $M=0$ invalidate the reduction?

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  • $\begingroup$ Can you define Disk Covering Problem you want to reduce from (which needs to be NP-Hard)? What are the instances of this problem? What are the yes-instances or the measure you want to optimize (which should depend on the instance)? $\endgroup$
    – Steven
    Commented Dec 4, 2023 at 19:42

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