The furthest-site geodesic voronoi diagram
We present anO((n+k) log(n+k))-time,O(n+k)-space algorithm for computing the furthest-site Voronoi diagram ofk point sites with respect to the geodesic metric within a simplen-sided polygon.
An equipartition of planar sets
We describe the "cobweb" partition scheme and show that it can split any planar set into eight regions of equal area.
The upper envelope of voronoi surfaces and its applications
Given a setS ofsources (points or segments) in 211C;d, we consider the surface in 211C;d+1 that is the graph of the functiond(x)=minp S (x, p) for some metric . This surface is closely related to the Voronoi diagram, Vor(S), ofS under the metric . The ...
On convex body chasing
A player moving in the plane is given a sequence of instructions of the following type: at stepi a planar convex setFi is specified, and the player has to move to a point inFi. The player is charged for the distance traveled. We provide a strategy for ...
The steiner minimal network for convex configurations
SupposeX is a convex configuration with radius of maximum curvaturer and at most one of the edges joining neighboring points has length strictly greater thanr. We use the variational approach to show the Steiner treeS coincides with the minimal spanning ...
