We show how any BSP tree TP for the endpoints of a set of n disjoint segments in the plane can be used to obtain a BSP tree of size O(n · depth(TP )) for the segments themselves, ...
We prove an optimal generalization of the centerpoint theorem: given a set P of n points in the plane, there exist two points (not necessarily among input points) that hit all con...
Given a set P of n points in the plane, we wish to find a set Q P of k points for which the convex hull conv(Q) has the minimum area. We solve this, and the related problem of fi...
We explore one method for finding the convex hull of certain mixed integer sets. The approach is to break up the original set into a small number of subsets, find a compact polyhed...
Given a convex polygon P with m vertices and a set S of n points in the plane, we consider the problem of nding a placement of P that contains the maximum number of points in S. W...