An Optical Simulation of Shared Memory

We present a work-optimal randomized algorithm for simulating a shared memory machine (PRAM) on an optical communication parallel computer (OCPC). The OCPC model is motivated by the potential of optical communication for parallel computation. The memory of an OCPC is divided into modules, one module per processor. Each memory module only services a request on a timestep if it receives exactly one memory request. Our algorithm simulates each step of an n lg lg n-processor EREW PRAM on an n-processor OCPC in O(lg lg n) expected delay. (The probability that the delay is longer than this is at most n sup (-alpha) for any constant alpha.) The best previous simulation due to Valiant required THETA (lg n) expected delay.