Parallel Algorithms on Three - Levelhierarchical Cubic

In this paper, we propose a novel interconnection network called three-level hierarchical cubic network (3-HCN), which extends the construction of hierarchical cubic networks (HCN) and ooers many additional advantages. The 3-HCN (with diameter links) has diameter smaller than that of an n-cube of the same size and uses nodes of degree 1 3 n + 2. We develop eecient and elegant algorithms for routing, broadcasting, semigroup computation, and matrix-matrix multiplication on 3-HCN. In particular, 3 p N 3 p N matrix-matrix multiplication can be performed in 1 3 log 2 N + 2 time, which is approximately one fth of that required for the DNS algorithm on the hypercube and HCN. We also develop algorithms for emulating a hyper-cube of the same size in O(1) time on 3-HCN. We present variants of 3-HCN that use diierent modules, such as tree, mesh, and buslet, to t the needs of various applications. We conclude that the 3-HCN and its variants are suitable for constructing high-performance special-purpose systems (e.g., for numerical computations) as well as cost-eeective general-purpose parallel architectures.