is a flat fish which swims using its huge side fins.

In many applications, only a small percentage of the points in a given set p of n points are extreme. in such a case, the convex hull of p has less than n vertices. this can actually make our algorithm convexhull run faster than θ(nlogn). assume, for instance, that the expected number of extreme points in a random sample of p of size r is o(rα ), for some constant α < 1. (this is true when the set p has been created by picking points uniformly at random in a ball.) prove that under this condition, the running time of the algorithm is o(n).