Efficient PRAM simulation on a distributed memory machine

Abstract

We present a randomized simulation of a nloglog(ra)log∗(n)-processor shared memory machine (PRAM) on an ra-processor distributed memory machine (DMM) with optimal expected delay 0(loglog(n)log∗ (n)) per step of simulation. The time bound for the delay is guaranteed with overwhelming probability. The algorithm is based on hashing and uses a novel simulation scheme. The best previous simulations use a simpler scheme based on hashing and have much larger expected delay: θ(log(n)/loglog(n)) for the simulation of an n-processor PRAM on an n-processor DMM, and θ(log(n))in the case where the simulation preserves the processor-time product.