PRAM Lower Bound for Element Distinctness Revisited

. This paper considers the problem of element distinctness on CRCW PRAMs with unbounded memory. A complete proof of the optimal lower bound of\Omega \Gamma n log n= \Gamma p log( n p log n + 1) \Delta\Delta steps for n elements problem on p processor COMMON PRAM is presented. This lower bound has been previously correctly stated by Boppana, but his proof was not complete. Its correction requires some additional observations and some not straightforward changes. 1 Introduction This paper considers the PRAM model with unbounded memory. A PRAM consists of p processors P 1 ; \Delta \Delta \Delta ; P p and shared memory with cells indexed by integers N . Initially the contents of all shared memory cells are 0 and processor P i , 1 i n, has the input value x i in it's local memory. One step of computation consists of three phases: local computation, global read, global write. On the PRIORITY model the minimal index processor (among those attempting to write to the same cell) succ..