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 1/2 the diameter of the equivalent hypercube, and that the average number of steps between processors for a Möbius cube is about 2/3 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 report results of simulation studies on the dynamic message-passing performance of the hypercube, the Twisted Cube of Hilbers et. al. [8], and the Möbius 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 Möbius cubes and in particular the 1-Möbius cube have better dynamic performance than the hypercube.
A longer version is available upon request from authors — Tech. Rept. 93-20-02.
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References
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© 1993 Springer-Verlag Berlin Heidelberg
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Cull, P., Larson, S.M. (1993). Static and dynamic performance of the Möbius cubes (short version). In: Bode, A., Reeve, M., Wolf, G. (eds) PARLE '93 Parallel Architectures and Languages Europe. PARLE 1993. Lecture Notes in Computer Science, vol 694. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56891-3_8
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DOI: https://doi.org/10.1007/3-540-56891-3_8
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