A theoretical network model and the Hamming cube networks

Abstract

We introduce a network model, called the Hamming group, which can be used to generate several important classes of hypercube-like topologies. The Hamming group is a specific group for which the Hamming-distance relations are used as the generators. This model enhanced with the unit incremental capability provides a framework for generating many possible supergraphs of incomplete hypercubes, having an arbitrary number of nodes. In particular, we derive from our model a new family of succinctly representable and labeled networks, called the Hamming cubes (HC's). These networks can recursively grow from the existing ones with the increment of one node at a time, have half of logarithmic diameter and are easily decomposable. Simple routing schemes are designed for Hamming cubes, which are optimally fault-tolerant since the node-connectivity is equal to the minimum degree. With respect to several topological and performance parameters, Hamming cubes are strong competitors of binary hypercubes or folded hypercubes. >