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Cost for traditional method

We can get each node to communicate with every other node in $N-1$ stages in which $N/2$ pairs of nodes simultaneously exchange packets of size $n u / N^2$ where $u$ is the size of a single data element (16 bytes for double precision complex).

\tau_{\rm trad} &=& 2 (N-1) \left[ \alpha + {n u \over \beta N...
...t] \\
&\approx& 2 \left[ \alpha N + {n u \over \beta N} \right]

Peter D. Haynes 2001-11-07