The Complexity of Deterministic PRAM Simulation on Distributed Memory Machines

In this paper we present lower and upper bounds for the deterministic simulation of a Parallel Random Access Machine (PRAM) with n processors and m variables on a Distributed Memory Machine (DMM) with p n processors. The bounds are expressed as a function of the redundancy r of the scheme (i.e., the number of copies used to represent each PRAM variable in the DMM), and become tight for any m polynomial in n and r = \Theta (1)