Section: New Results
On Order Types of Random Point Sets
Participant : Marc Glisse.
In collaboration with Olivier Devillers and Xavier Goaoc (Inria team Gamble) and Philippe Duchon (LaBRI, Université de Bordeaux).
Let be a set of random points chosen uniformly in the unit square. In this paper , we examine the typical resolution of the order type of . First, we show that with high probability, can be rounded to the grid of step without changing its order type. Second, we study algorithms for determining the order type of a point set in terms of the number of coordinate bits they require to know. We give an algorithm that requires on average bits to determine the order type of , and show that any algorithm requires at least bits. Both results extend to more general models of random point sets.