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All-to-all communication is a well known performance bottleneck for many applications, such as the ones that use the Fast-Fourier-transform (FFT) algorithm. We analyze the performance of all-to-all communication on the BlueGene/L torus interconnect that has link contention even for all-to-all operations with short messages. We observed that the performance of all-to-all depends on the shape of the processor partition. We present a performance analysis of all-to-all on partitions of various shapes. We then present optimization schemes that substantially improve the performance of all-to-all with short and large messages.In particular, throughput improved from 64% to over 99% of peak on the 65,536 (64 times 32 times 32) node Blue Gene/L machine at the Lawrence Livermore National Lab. We show the impact of the all-to-all performance optimizations in 1-D and 3-D FFT benchmarks. We achieved a performance of over 2.8 TF for the HPC Challenge 1D FFT benchmark with our optimized all-to-all.
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Kumar et al. (2008) studied this question.