This paper looks at axioms for convexity, and shows how they can be applied to discrete spaces. Two structures for a discrete geometry are considered: oriented matroids, and cell c...
We propose a linear in time and easy-to-implement algorithm that robustly decomposes a digital curve into convex and concave parts. This algorithm is based on classical tools in d...
Steinitz’s Theorem states that a graph is the 1-skeleton of a convex polyhedron if and only if it is 3-connected and planar. The polyhedron is called a geometric realization of ...
Dan Archdeacon, C. Paul Bonnington, Joanna A. Elli...
We develop improved risk bounds for function estimation with models such as single hidden layer neural nets, using a penalized least squares criterion to select the size of the mod...
We describe an algorithm for computing planar convex hulls in the self-improving model: given a sequence I1, I2, . . . of planar n-point sets, the upper convex hull conv(I) of eac...
Kenneth L. Clarkson, Wolfgang Mulzer, C. Seshadhri