An algebraic theory for modeling direct interconnection networks

The authors present an algebraic theory based on tensor products for modeling direct interconnection networks. This theory has been used for designing and implementing block recursive numerical algorithms on shared-memory vector multiprocessors. This theory can be used for mapping algorithms expressed in tensor product form onto distributed-memory architectures. The authors focus on the modeling of direct interconnection networks. Rings, n-dimensional meshes, and hypercubes are represented in tensor product form. Algorithm mapping using tensor product formulation is demonstrated by mapping matrix transposition and matrix multiplication onto different networks