Recursive hierarchical swapped networks: versatile interconnection architectures for highly parallel systems

Abstract

The authors propose a new class of interconnection networks called recursive hierarchical swapped networks (RHSN) for general-purpose parallel processing. The node degrees of RHSNs can vary from a small number to as large as required, depending on recursive and hierarchical composition parameters and the nucleus graph chosen. The diameter of an RHSN can be asymptotically optimal within a small constant factor. They present efficient routing, semigroup computation, ascend/descend, matrix-matrix multiplication, and emulation algorithms, thus proving the versatility of RHSNs. In particular on suitably constructed RHSNs, matrix multiplication can be performed faster than the DNS algorithm on a hypercube. Furthermore, ascend/descend algorithms, semigroup computation, and parallel prefix computation can be done using algorithms with asymptotically fewer communication steps than on a hypercube.