Topological Properties of Generalized Banyan-Hypercube Networks

Abstract This paper discusses the topological properties of a recently introduced family of networks, called the banyan-hypercubes (BH), and defines a family of generalized banyan-hypercubes. A banyan-hypercube, denoted BH (h, k, s), is constructed by taking the bottom h levels from the base of a rectangular banyan of spread s and sk nodes per level for s a power of 2, and interconnecting the nodes at each level in a hypercube. The banyan-hypercubes can be viewed as a scheme for interconnecting hypercubes while keeping most of the advantages of the latter. In this paper, the definition of BHs will be extended and generalized to (1) allow the interconnection of an unlimited number (h) of hypercubes and (2) allow any h successive levels of the banyan to interconnect hypercubes. This leads to better extendability and flexibility in partitioning. The diameter and average distance of the generalized BH are derived and shown to provide an improvement over the hypercube for a wide range of values for h, k, and s. Self-routing point to point and broadcasting algorithms are presented and efficient embeddings of various networks, on the BH, can be constructed.