Mapping rings and grids onto the FPS T-series hypercube

One of the desirable aspects of a hypercube is that many other interconnection topologies are contained within it. Two commonly used topologies are the ring and two-dimensional grid. The mapping of these topologies onto the hypercube is straightforward, but in the FPS T-Series hypercube, algorithms using the standard mapping based on binary reflective Gray codes will not perform well. This is because the standard mapping requires the use of communication links that, in some of the nodes, cannot be communicated on simultaneously. In such nodes, a very time consuming reset of the link configuration is necessary between every use of the conflicting links. For many algorithms, this resilts in a large overhead and degrades performance. In this paper it is shown how to configure the links in each node once to map a ring and grid onto the T-Series, thereby eliminating the overhead of resetting the links repeatedly during execution. The mappings are extended to a more general class of hypercube called modulus link-bounded hypercubes, and various properties of the mappings are presented