Suppose we are given a finite set of points P in R3 and a collection of polytopes T that are all translates of the same polytope T. We consider two problems in this paper. The firs...
Let S be a finite set of n + 3 points in general position in the plane, with 3 extreme points and n interior points. We consider triangulations drawn uniformly at random from the...
The celebrated upper bound theorem of McMullen determines the maximal number of extreme points of a polyhedron in terms of its dimension and the number of constraints which define...
This paper focuses on the assignment of discrete points among K robots and determining the order in which the points should be processed by the robots, in the presence of geometric...
Nilanjan Chakraborty, Srinivas Akella, John T. Wen
Given n points in the plane, we study three optimization problems of computing an empty pseudo-triangle: we consider minimizing the perimeter, maximizing the area, and minimizing ...