A Formal Study of the Mcube Interconnection Network

The Mcube network has been proposed in [11] as a highly recursive and symmetrical interconnection network based on twisted links [1]. The Mcube topology has been developed and defined in terms of the structural constraints between components to enforce structural symmetry instead of specifying edges between node pairs. Mcubes have almost half the diameter of a comparable hypercube, a lower average internode distance than most other twisted networks and an uniform spatial node distribution. Unlike most twisted cube–based networks, randomly destined traffic results in uniform traffic flow through every node in the Mcube and links in the Mcube saturate more slowly than hypercubes. The Mcube is recursively partitionable and allows several parallel algorithms to execute as fast as or faster than on a hypercube. We establish the node distribution for the Mcubes to be uniform with the internode distance. Based on the constraints imposed by the construction and the routing algorithm, we derive an expression for the average internode distance for Mcubes. We also introduce an efficient broadcasting algorithm for the Mcube interconnection and show how Mcubes can be reconfigured into hypercubes. Finally, we show how representative parallel algorithms can be directly implemented on the Mcube topology.