VC-Dimension of Visibility on Terrains
نویسنده
چکیده
A guarding problem can naturally be modeled as a set system (U ,S) in which the universe U of elements is the set of points we need to guard and our collection S of sets contains, for each potential guard g, the set of points from U seen by g. We prove bounds on the maximum VC-dimension of set systems associated with guarding both 1.5D terrains (monotone chains) and 2.5D terrains (polygonal terrains). We prove that for monotone chains, the maximum VC-dimension is 4 and that for polygonal terrains, the maximum VC-dimension is unbounded.
منابع مشابه
On the VC-Dimension of Visibility in Monotone Polygons
We show that the VC-dimension of visibility on the boundary of a monotone polygon is exactly 6. Our lower bound construction matches the best known lower bound for simple polygons.
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