Topological properties of banyan-hypercube networks

Topological properties of banyan-hypercubes are discussed, and a family of generalized banyan-hypercubes is defined. A banyan-hypercube, denoted BH(h, k, s), is constructed by taking the bottom h levels of a rectangular banyan of spread s and s^k nodes per level for s a power of two, and interconnecting the nodes at each level in a hypercube. BHs can be viewed as a scheme for interconnecting hypercubes while keeping most of the advantages of the latter. The definition of BHs is extended and generalized to allow the interconnection of an unlimited number of hypercubes and to allow any h successive levels of the banyan to interconnect hypercubes. This leads to better extendibility and flexibility in partitioning the BH. The diameter and average distance of the generalized BH are derived and are shown to provide an improvement over the hypercube for a wide range of h, k, and s values. Self-routing point-to-point and broadcasting algorithms are presented, and efficient embeddings of various networks on the BH are shown