The Mobius cubes are hypercube variants that give better performance with the same number of links and processors. We show that the diameter of the Mobius cubes is about one half the diameter of the equivalent hypercube, and that the average number of steps between processors for a Mobius cube is about two-thirds of the average for a hypercube. We give an efficient routing algorithm for the Mobius cubes. This routing algorithm finds a shortest path and operates in time proportional to the dimension of the cube. We also give efficient broadcast algorithms for the Mobius cubes. We show that the Mobius cubes contain ring networks and other networks. We report results of simulation studies on the dynamic message-passing performance of the hypercube, the Twisted Cube of P.A.J. Hilbers et al. (1987), and the Mobius cubes. Our results are in agreement with S. Abraham (1990), showing that the Twisted Cube has worse dynamic performance than the hypercube, but our results show that the 1-Mobius cube has dynamic performance superior to that of the hypercube. This contradicts current literature, which implies that twisted cube variants will have worse dynamic performance.>

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.