Allgather by Logarithmic Expansion


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In general the math looks like:

Assume you have MATH processes with $\QTR{Large}{i+j=m}$ . Assume each block of MATH nodes have gathered their data.

Let $\QTR{Large}{n}$ be even MATH $\QTR{Large}{-2}$.

In the next step MATH and MATH exchange , hence gather, their data.

For in MATH and MATH $\QTR{Large}{-1.}$

MATH