A problem in distance geometry is to find the location of an unknown point in a given convex set in Rk such that its farthest distance to n fixed points is minimum. In this paper we present an algorithm based on subgradient method and convex hull computation for solving this problem. A recent improvement of Quickhull algorithm for computing the convex hull of a finite set of planar points is ap...

For a finite set of points X on the unit hypersphere in R we consider the iteration ui+1 = ui +χi, where χi is the point of X farthest from ui. Restricting to the case where the origin is contained in the convex hull of X we study the maximal length of ui. We give sharp upper bounds for the length of ui independently of X . Precisely, this upper bound is infinity for d ≥ 3 and √ 2 for d = 2.

We present optimal parallel algorithms that run in O(p n) time on a p n p n mesh-connected computer for a number of fundamental problems concerning visibility and distance properties inside a simple polygon. These include computing shortest paths, shortest path trees, shortest path partitions, all-farthest neighbors (both internal and external), the visibility polygon of a point, the weak visib...

We present optimal parallel algorithms that run in O p n time on a p n pn mesh connected computer for a number of fundamental problems concerning proximity and vis ibility in a simple polygon These include computing shortest paths shortest path trees shortest path partitions all farthest neighbors the visibility polygon of a point the weak visibility polygon of an edge and the ray shooting problem