Improved optimal shared memory simulations, and the power of reconsideration

We present time-processor optimal randomized algorithms for simulating a shared memory machine (EREW PRAM) on, a distributed memory machine (DMM). The first algorithm simulates each step of an n-processor EREW PRAM on an n-processor DMM with O(log log n/log log log n) delay with high probability. This simulation is work optimal and can be made time-processor optimal. The best previous optimal simulations require O(log log n) delay. We also study reconfigurable DMMs which are a “complete network version” of the well studied reconfigurable meshes. We show an algorithm that simulates each step of an n-processor EREW PRAM DMM an n-processor reconfigurable DMM with only O(log* n) delay with high probability. We further show how to make this simulation time-processor optimal