Optimal cube-connected cube multicomputers

Many CFD (computational fluid dynamics) and other scientific applications can be partitioned into subproblems. However, in general, the partitioned subproblems are very large. They demand high-performance computing power themselves, and their solutions have to be combined at each time step. In this paper, the cube-connect cube (CCCube) architecture is studied. The CCCube architecture is an extended hypercube structure with each node represented as a cube. It requires fewer physical links between nodes than the hypercube, and provides the same communication support as the hypercube does on many applications. The reduced physical links can be used to enhance the bandwidth of the remanding links and, therefore, enhance the overall performance. The concept and the method to obtain optimal CCCubes, which are the CCCubes with a minimum number of links under a given total number of nodes, are proposed. The superiority of optimal CCCubes over standard hypercubes has also been shown in terms of the link usage in the embedding of a binomial tree. A useful computation structure based on a semi-binomial tree for divide-and-conquer type of parallel algorithms has been identified. We have shown that this structure can be implemented in optimal CCCubes without performance degradation compared with regular hypercubes. The result presented in this paper should provide a useful approach to design of scientific parallel computers.