3.3.2 Gather-Scatter operations

Gathering (assemble) or scattering (distribute) of data by an excellent process, in the following called root process.

• Let the number of the root process be 0.
• The optimal tree is embedded in the hypercube (Sec. 2.2.6)
• Scatter $\Longrightarrow$ TREE/SMALL>_DOWN($nWords$,$Data$)
• Gather $\Longrightarrow$ TREE/SMALL>_UP($nLocal$,$DataIn$,$nOut$,$DataOut$,$MaxData$)

If nCube denotes the dimension of a hypercube and ICH is the number of a process therein, then TREE/SMALL>_DOWN can be realized as follows.
In algorithm 3.1, the load of the link connections rises with increasing link number.