The hierarchical hypercube: a new interconnection topology for massively parallel systems

Interconnection networks play a crucial role in the performance of parallel systems. This paper introduces a new interconnection topology that is called the hierarchical hypercube (HHC). This topology is suitable for massively parallel systems with thousands of processors. An appealing property of this network is the low number of connections per processor, which enhances the VLSI design and fabrication of the system. Other alluring features include symmetry and logarithmic diameter, which imply easy and fast algorithms for communication. Moreover, the HHC is scalable; that is it can embed HHC´s of lower dimensions. The paper presents two algorithms for data communication in the HHC. The first algorithm is for one-to-one transfer, and the second is for one-to-all broadcasting. Both algorithms take O(log₂ k), where k is the total number of processors in the system. A wide class of problems, the divide & conquer class (D&Q), is shown to be easily and efficiently solvable on the HHC topology. Parallel algorithms are provided to describe how a D&Q problem can be solved efficiently on an HHC structure. The solution of a D&Q problem instance having up to k inputs requires a time complexity of O(log₂ k)