An optimal parallel algorithm for solving the maximal elements problem in the plane

We describe an O(log(n)) time with O(n) processors optimal algorithm for finding the maximal elements of a set. The model of parallel computation we consider is the CREW-PRAM, i.e. it is the synchronous shared memory model where concurrent reads are allowed but no two processors can simultaneously attempt to write in the same memory location (even if they are trying to write the same thing).