# Understanding PAM - why is it greedy?

I've been studying k-medoids for a while but i can't understand the first step or BUILD step: in particular i can't get how the initial medoids would be "greedy". I'm not much confident with the theory behind this notion but i can guess what does it mean. I understand from other answers in here that first medoid is chosen as the medoid of the whole dataset and this is "greedy", but how about the other $$k-1$$? I really can't consider random choice of the other medoids as "greedy". So my question is about how the initial $$k$$ medoids are picked, except the random choice k-means like. And then, is it right to consider PAM an approximation of k-medoids problem that performs a greedy search (that provides an approximate solution, of course)?