A linear equation model for twisted cube networks

The Twisted 3-cube is an interconnection network that twists the edges of the 3-dimensional hypercube to produce a network with diameter 2 and expected distance 11/8. A number of papers have shown that the Twisted 3-cube can be generalized into higher dimensional cube-like networks. We show that many of these networks can be described using a simple model. We place bounds on the diameter and expected distances of networks in this model, and show that the dynamic performance of these networks can match or improve upon the hypercube's performance in most conditions.