When we are mapping nodes to processors we work with ( ranges) of
processors at each step, denoted [a, b]. So we begin with processors
[1, n], where n is the total number of processors involved in the
computation. We assume that we have a subdividing function
Subsection(r, p, q) that divides r into q subsections and
returns the pth. We also need another function Lastsection(r,
p, q) , that divides r into q sub sections and returns the
sections 
as one combined range. We assume that the
directions in each level are numbered so that the directions that do
not commute with any of the others are placed first. We take a path
p and calculate which processor to allocate it to.
![\begin{figure}
\begin{verbatim}
Range r = [1, n]
i = first direction in p
while(...
...ree)
i -\gt next direction in p
}
return minimum of r\end{verbatim}\end{figure}](img41.gif)