I have this problem described in natural language, and I was wondering whether it is relatable to any known problem.
I have a directed acyclic graph. Each node can host a "probe". If node $i$ hosts a probe, then node $i$ and all the nodes connected to $i$ are considered "probed". I have to place a number $p$ of probes to maximize the number of probed nodes.
It reminds me of a covering problem, but on a network: so I was wondering if there is something more specific about this or it is just a matter of abstracting the natural language description. I am mainly interested in MILP formulations, but other pointers are welcome as well.