Consider a preemptive priority scheduling algorithm based on dynamically changing priorities. greater priority number implies higher priority. when a process is waiting for the cpu (in the ready queue, but not running), its priority changes at a rate w; when it is running, its priority changes at a rate r. all processes are given a priority of 0 when they enter the ready queue. explain how the processes are scheduled (that is, how they are ordered) when 0> w> r.

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).