Analysis of a cluster-based architecture for hypercube multicomputers

In this dissertation, we propose and analyze a cluster-based hypercube architecture in which each node of the hypercube is furnished with a cluster of n processors connected through a small crossbar switch with n memory modules. Topological analysis of the cluster-based hypercube architecture shows that it reduces the complexity of the basic hypercube architecture by reducing the diameter, the degree of a node and the number of links in the hypercube. The proposed architecture uses the higher processing power furnished by the cluster of execution processors in each node to address the needs of computation-intensive parallel application programs. It provides a smaller dimension hypercube with the same number of execution processors as a higher dimension conventional hypercube architecture. This scheme can be extended to meshes and other architectures. Mathematical analysis of the parallel simplex and parallel Gaussian elimination algorithms executing on the cluster-based hypercube show the order of complexity of executing an n x n matrix problem on the cluster-based hypercube using parallel simplex algorithm to be O(n^2) and that of the parallel Gaussian elimination algorithm to be O(n^3). The timing analysis derived from the mathematical analysis results indicate that for the same number of processors in the cluster-based hypercube system as the conventional hypercube system, the computation to communication ratio of the cluster-based hypercube executing a matrix problem by parallel simplex algorithm increases when the number of nodes of the cluster-based hypercube is decreased. Self-driven simulations were developed to run parallel simplex and parallel Gaussian elimination algorithms on the proposed cluster-based hypercube architecture and on the Intel Personal Supercomputer (iPSC/860), which is a conventional hypercube. The simulation results show a response time performance improvement of up to 30% in favor of the cluster-based hypercube. We also observe that for increased link delays, the performance gap increases significantly in favor of the cluster-based hypercube architecture when both the cluster-based hypercube and the Intel iPSC/860, a conventional hypercube, execute the same parallel simplex and Gaussian elimination algorithms.