Hunting Voronoi vertices

Hunting Voronoi Vertices

An iterative algorithm for the determination of voronoi vertices in polygonal and non-polygonal domains

We propose a new iterative algorithm for the computation of the vertices of a Voronoi diagram for a set of geometric objects of the euclidean plane. Each one of these vertices is the centre of the circle “touching” a triple of objects (passing through points or tangent to any other geometric object). The algorithm starts with an initial triple of points pertaining to each one of the three objec...

Mutualistic hunting

The cooperative acquisition, defense and distribution of meat are common problems that must be solved by social hunters. These were also problems faced by any of our hominid ancestors that may have hunted large game in our evolutionary past. Much of the last 40 years of research in evolutionary ecology has tried to understand such cooperative behavior. The classic Prisoner's Dilemma game theory...

Hunting dimers

HBCBH and HAlCAlH are related electrondeficient molecules, predicted as local minima on their respective potential energy surfaces. Different views of their electronic structure—as allenes, carbenes, or carbones—prompted two research groups to a friendly competition exploring the predilection of these small molecules to dimerize. Many such dimers emerged from the calculations, some with large e...

Forbidden Vertices

In this work, we introduce and study the forbidden-vertices problem. Given a polytope P and a subset X of its vertices, we study the complexity of linear optimization over the subset of vertices of P that are not contained in X . This problem is closely related to finding the k-best basic solutions to a linear problem. We show that the complexity of the problem changes significantly depending o...