Erd˝os, Purdy, and Straus conjectured that the number of distinct (nonzero) areas of the triangles determined by n noncollinear points in the plane is at least n−1 2 , which is...
The (axis-parallel) stabbing number of a given set of line segments is the maximum number of segments that can be intersected by any one (axis-parallel) line. We investigate probl...
We show that there is a constant > 0 such that, for any set P of n 5 points in general position in the plane, a crossing-free geometric graph on P that is chosen uniformly at...
We introduce a new feature size for bounded domains in the plane endowed with an intrinsic metric. Given a point x in a domain X, the homotopy feature size of X at x measures half...
Jie Gao, Leonidas J. Guibas, Steve Oudot, Yue Wang
In this paper, we propose an algorithm for computing the farthest-segment Voronoi diagram for the edges of a convex polygon and apply this to obtain an O(n log n) algorithm for th...