COMPLEXITY OF PARALLEL SORTING.

The model we consider is the (concurrent-write, PRIORITY) PRAM. It has n synchronous processors, which communicate via an infinite shared memory. When several processors simultaneously write to the same cell, the one with the largest index succeeds. We allow the processors arbitrary computational power. Our main result is that sorting n integers requires OMEGA ( ROOT log n) steps in this strong model. This bound is proved in two stages. First, using a novel Ramsey theoretic argument, we 'reduce' sorting on a PRAM to sorting on a parallel merge tree. This tree is a generalization of Valiant's parallel comparison tree from left bracket V right bracket in which at every step n pairs of (previously ordered) sets are merged (rather then n pairs of elements compared). The second stage is proving the lower bound for such trees.