General asynchrony is not expensive for PRAMs

The authors present a technique to efficiently simulate a synchronous n-processor PRAM using a completely asynchronous PRAM. This work is an extension of prior results of Martel et. al. (1990) in which a measure of work for asynchronous PRAM algorithms is developed that accounts for all instructions executed by the processors including busy waiting steps. These prior results show that if the asynchrony is modestly restricted, the expected work of asynchronous PRAM algorithms is within a constant factor of the expected work on a standard synchronous n-processor PRAM. They extend these prior results to a general asynchronous model with only O(nT(min(log P,log U))) expected work and O(nT) space, using up to n/lognlog*n processors. Here, P is the number of processors used in the simulation, U is the maximum number of updates to any single data item, and T is the number of time steps in the synchronous n-processor PRAM algorithm. The results indicate that completely relaxing synchrony in shared memory parallel processing systems is possible with only modest additional work