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The Naive Ratio of Communication in three distributions is:
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| 2 |
64 : 16 : 12 for One : Two : Three Dimensional Decompositions
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| 3 |
Three dimensions also has lower pipelining start-up effects
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| 4 |
However -- certainly for one dimensional case -- it is better to redistribute data before sweep that crosses processor boundaries
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Total Algorithm Communication cost 643 Units
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For a redistribution that reduces algorithm communication cost to zero, one has redistribution cost that is proportional to 642 (Number of elements per processor) times a number which depends on communication network -- this number is loge64=6 for a hypercube
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