Section:
New Results
Miscellaneous
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 [41], 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.