The REFINE Multiprocessor - Theoretical Properties and Algorithms

A reconfigurable interconnection network based on a multi-ring architecture called REFINE is described. REFINE embeds a single l-factor of the Boolean hypercube in any given configuration. The mathematical properties of the REFINE topology and the hardware for the reconfiguration switch are described. The REFINE topology is scalable in the sense that the number of interprocessor communication links scales linearly with network size whereas the network diameter scales logarithmically with network size. Primitive parallel operations on the REFINE topology are described and analyzed. These primitive operations could be used as building blocks for more complex parallel algorithms. A large class of algorithms for the Boolean n-cube which includes the FFT and the Batcher’s bitonic sort is shown to map efficiently on the REFINE topology. The REFINE multiprocessor is shown to offer a cost-effective alternative to the Boolean n-cube multiprocessor architecture without substantial loss in performance.