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Covering Polygons is Even Harder
In the MINIMUM CONVEX COVER (MCC) problem, we are given a simple polygon $\mathcal P$ and an integer $k$, and the question is if there exist $k$ convex polygons whose union is $\mathcal P$.
Training Neural Networks is ER-complete
Given a neural network, training data, and a threshold, finding weights for the neural network such that the total error is below the threshold is known to be NP-hard.
Training Neural Networks is $\exists\mathbb R$-complete
Given a neural network, training data, and a threshold, it was known that it is NP-hard to find weights for the neural network such that the total error is below the threshold.
How to Cut Corners and Get Bounded Convex Curvature
A region of points in the plane $Q$ has \emph{bounded convex curvature} if for any point $x\in\partial Q$, there is a unit disk $U$ and $\varepsilon>0$ such that $x\in \partial U$ and all points in $U$ within distance $\varepsilon$ from $x$ are in $Q$.
Computational Geometry
