Efficient Asynchronous Simulation of a Class of Synchronous Parallel Algorithms

摘要

Several recent papers have introduced asynchronous shared memory parallel models in an attempt to discover how removing the assumption of synchronization of processor steps may alter the parallel complexities of problems. Preliminary work has resulted in the development and analysis of algorithms for a few specific problems. The best known general technique for transforming synchronous algorithms into asynchronous ones has been to synchronize all processors after each step of a synchronous computation. This results in the time complexity being multiplied by a factor that may be logarithmic in the number of processors, where time is defined to be the expected maximum numbers of steps taken by any processor, with respect to several families of distributions on processor schedules. Here we give a transformation technique that forms an asynchronous algorithm that runs in O(t + log p) time using p processors from any synchronous algorithm that runs in O(t) time on a p-processor CROW PRAM. This result can be extended to more general classes of synchronous algorithms. The technique yields an O(log p) time algorithm for p-input sorting, making possible the simulation of algorithms that run on the PRIORITY CRCW PRAM.