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).

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