A new approach to hypercube network analysis

A bit-positional notation is proposed for representing the interconnection topology of a hypercube. This approach greatly helps in the analysis of basic properties of a hypercube network. Some systematic procedures are derived to expand binary trees and map them into higher-dimensional hypercubes. The authors show that an n-cube network can be enhanced by adding at most 2^n-2 diagonal links, which makes it possible to map a complete binary tree into a hypercube with any one of its nodes as the root. The problem of mapping mesh networks into hypercube networks is discussed