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The Möbius Cubes
May 1995 (vol. 44 no. 5)
pp. 647-659

Abstract—The Möbius cubes are hypercube variants that give better performance with the same number of links and processors. We show that the diameter of the Möbius cubes is about one half the diameter of the equivalent hypercube, and that the average number of steps between processors for a Möbius cube is about two-thirds of the average for a hypercube. We give an efficient routing algorithm for the Möbius 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 Möbius cubes. We show that the Möbius 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 Hilbers et al. [11], and the Möbius cubes. Our results are in agreement with Abraham [2], showing that the Twisted Cube has worse dynamic performance than the hypercube, but our results show that the 1-Möbius 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.

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Index Terms:
Graph theory, hypercube, interconnection network, message routing, parallel architecture.
Citation:
Shawn M. Larson, Paul Cull, "The Möbius Cubes," IEEE Transactions on Computers, vol. 44, no. 5, pp. 647-659, May 1995, doi:10.1109/12.381950
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