Abstract
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 1/2 the diameter of the equivalent hypercube, and that the average number of steps between processors for a Mobius cube is about 2/3 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 report results of simulation studies on the dynamic message-passing performance of the hypercube, the Twisted Cube of Hilbers et. al. [8], and the Mobius cubes. Our results agree with those of Abraham [2], showing that the Twisted Cube has worse dynamic performance than the hypercube. But our results show that the Mobius cubes and in particular the 1-Mobius cube have better dynamic performance than the hypercube.
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