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 n-processor CRCW PRAM on an n-processor DMM with \(\mathcal{O}\)log log log 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 \(\mathcal{O}\)(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.KeywordsHash FunctionShared MemoryIncident EdgeSimple PathParallel Random Access MachineThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.