Suppose I'm given a connected polygon in the plane with holes. I can "remove" a hole by drawing a straight line from the boundary of a hole to another boundary (either of another hole, or the boundary separating the polygon from the exterior).
Let's say the "cost" of a cut is its length. What is the minimum cost set of cuts needed to remove all holes in a polygon ?
At first I thought this would be easy: write down the distances between each pair of holes and each hole and the polygon boundary, and compute an MST. But it's not obvious to me that this is correct.
Is this a known problem ?