Highway hull revisited

Highway hull revisited

A highway H is a line in the plane on which one can travel at a greater speed than in the remaining plane. One can choose to enter and exit H at any point. The highway time distance between a pair of points is the minimum time required to move from one point to the other, with optional use of H. The highway hull H(S,H) of a point set S is the minimal set containing S as well as the shortest pat...

Sweep Line Algorithm for Convex Hull Revisited

Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and imp...

Highway Engineering Highway Engineering

QUICKSELECT Revisited

We give an overview of the running time analysis of the random divide-and-conquer algorithm FIND or QUICKSELECT. The results concern moments, distribution of FIND’s running time, the limiting distribution, a stochastic bound and the key: a stochastic fixed point equation.

The Local Polynomial Hull near a Degenerate Cr Singularity – Bishop Discs Revisited

Let S be a smooth real surface in C and let p ∈ S be a point at which the tangent plane is a complex line. Many problems in function theory depend on knowing whether S is locally polynomially convex at such a p — i.e. at a CR singularity. Even when the order of contact of Tp(S) with S at p equals 2, no clean characterisation exists; difficulties are posed by parabolic points. Hence, we study no...