10.6 NODE PROJECTION OPERATION
In Section 10.5, we discussed how we can associate a time step value to each point in the computation domain 
. In this section, we discuss how we can assign a processor or a thread to each point in the DAG. The combination of node scheduling and node projection will result in determination of the work done by each task at any given time step. The choice of the projection operation will impact the interthread or interprocessor communication, which is a very crucial factor in determining the speed of the execution of the algorithm.
The projection operation transforms our DAG in 
to a projected DAG in an integer space of reduced dimensionality 
where k < n. We label the new projected acyclic graph 
. Central to the projection operation is the projection matrix P and the projection direction d.
A subtle point to be noticed in the projection operation is that it controls the amount of workload assigned to each software thread for a multithreaded implementation or the workload assigned to each PE for a systolic array implementation. Just like affine scheduling, ...
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