Correlation of Data Exchange with Partitioning Sample Clauses

Correlation of Data Exchange with Partitioning. We compared the communication graph D with its corresponding partitioning graph M generated by the partitioner and observed, as expected, a close correlation: the more shared entities between partitions (the larger the weight Mi j), the more data is exchanged by the processes i and j. We applied a regression model to discover how accurately the volume of exchanged data can be predicted based on data provided by the partitioner. More specifically, by letting β0 and β1 be the regression coefficients, we build an estimator H c D such that H = β0W + β1M + E , where AllToAll is the matrix with all entries equal to 1 representing all-to-all collective communications and E stands for the unknown communication pattern introduced by the preconditioner. We find β0 and β1 by minimizing the 2-norm of the residual matrix D − H . In our regression model, we ignored E since it is not readily quantifiable and we estimated β0 ≈ .3 and β1 ≈ .7 with an the r-squared value of almost 90%.
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