Shared memory simulations with triple-logarithmic delay

Abstract

We consider the problem of simulating a PRAM on a distributed memory machine (DMM). Our main result is a randomized algorithm that simulates each step of an w-processor CRCW PRAM on an n-processor DMM with O(log loglog n log* n) delay, with high probability. This is an exponential improvement on all previously known simulations. It can be extended to a simulation of an (n log log log n log* n)-processor EREW PRAM on an n-processor DMM with optimal delay O(log log log n log* n), with high probability. Finally a lower bound of Ω(log log log n/log log log log n) expected time is proved for a large class of randomized simulations that includes all known simulations.