The 'Mobius cubes': improved cubelike networks for parallel computation

Abstract

The Mobius cubes are created, by rearranging in a systematic manner, some of the edges of a hypercube. This rearrangement results in smaller distances between processors; where distance is the number of communication links which must be traversed. The authors show that the n-dimensional Mobius cubes have a diameter of about n/2 and expected distance of about n/3. These distances are a considerable savings over the diameter of n and expected distance of n/2 for the n-dimensional hypercube. The authors show that the Mobius cubes have a slightly more complicated algorithm than the hypercube. While the asymmetry of the Mobius cubes may give rise to communications bottlenecks, they report preliminary experiments showing the bottle necks are not significant. They compare their Mobius cubes to other variants and indicate some advantages for the Mobius cubes.<>