Parallel routing algorithms for incomplete hypercube interconnection networks

Abstract

Hypercube interconnection networks have been receiving considerable attention in the supercomputing environment. However, the number of processors must be exactly 2 r for an r-cube complete hypercube. This restriction severely limits its applicability. In this paper, we address three variant hypercube topologies with more flexibility in system sizes, the labelled hypercubes I m r , I M r , and I A r . Incomplete hypercube I m r consists of an r-cube and an m-cube complete hypercubes; I m r is composed of 2 r and Σ m ϵ M 2 m nodes; I Ar comes from an r-cube complete hypercube which operates in a degraded manner and allows that the missing nodes to be arbitrarily distributed. Specifically, we focus on the parallel paths routing algorithms for these three classes of incomplete hypercubes. Parallel paths between any given two nodes mean that these paths have the same source and destination nodes but with different intermediate nodes. Parallel communication is important as it will allow us to use the full bandwidth of the multiprocessors for the data transfer operation between any two nodes, and3these redundant paths can increase system fault-tolerance and communication reliability. With these parallel routing algorithms, one can use them as a criterion to design multiprocessor systems.