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Conclusions

This type of topology will almost always require the use of the CYCLIC(N) directive in the data distribution. Because of the symmetry inherent in this type of application and the fact that some compilers do not compile or perform well when using the (CYCLIC(N),CYCLIC(M)) distribution (a cyclic distribution over both dimensions), the use of the (*,CYCLIC(N)) technique is recommended. Further, the size of column blocks N to be used should chosen such that the edge over area ratio x is in the range . The size of the blocks in this case is such that load balancing in nearly perfect but the edge over area ratio is not unnecessarily large. The experiment bares this out, as the best distribution (*,CYCLIC(20)) has an edge over area ratio of 0.12. It is important to note that depending on the number of processors used, this ratio may correspond to a (*,BLOCK) distribution. If a (*,BLOCK) distribution yields a larger ratio than this to start with, the problem size is probably not large enough to justify that many processors in the first place.



Michael McMahon
Thu Dec 19 11:06:39 EST 1996