This constraint ensures that the relationship between data and computation
from Eqn. 3 holds.
If two iterations 
and 
in loop nest j
are mapped to the same processor, then the data of array x they access must
also be mapped to the same processor.
For 
, then from
section 3, 
.
Using Eqn. 3: 
and thus 
.
Formally,
Similarly, two iterations 
and 
in loop
nest j must be mapped to
the same processor if the data of array x they access are mapped to the
same processor.
Again, let 
.
If 
then 
.
Since 
,
if 
then the two iterations reference the
same array location and must be mapped to the same processor.
Let 
.
In general,
The sequential loops in each loop nest cause elements of the array referenced in that loop nest to be allocated local to the same processor. The local array elements cause iterations of the loop nests that access those elements to be executed sequentially.
