We develop an analytical model of grid communication on the connection machine for arbitrary grid geometries over exact power-of-two distances. There is excellent agreement between the model and the measured performance of the CM2. We propose some conceptually simple enhancements to the virtual processor mechanism and to the grid communication microcode which could lead to substantial performance improvements for several important numerical algorithms.

The parallelizing compiler for the B-HIVE loosely-coupled multiprocessor system uses a medium grain model to minimize the communication overhead. A medium grain model is shown to be an optimum way of merging fine grain operations into parallel tasks such that the parallelism obtained at the grain level is retained and communication overhead is decreased. A new communication model is introduced in this paper, allowing additional overlap between computation and communication. Simulation results indicate that the medium grain communication model shows promise for automatic parallelization for a loosely-coupled multiprocessor system.