18.5 DAG NODE PROJECTION
The projection operation is a many-to-one function that maps several nodes of the DAG onto a single node. Thus, several operations in the DAG are mapped to a single node or task. The projection operation allows for software thread economy or hardware economy by multiplexing several operations in the DAG on a single thread or processing element, respectively. For a 2-D DAG we are able to achieve node projection by choosing proper projection direction d. The author provided an extensive treatment of the projection operation in [86] and in Chapters 10 and 11.
The projection direction d projects a point p in the 2-D DAG to a point 
on a line such that
(18.20)
where P is a the projection matrix of dimension 1 × 2, which is in our case a vector normal to d. A valid projection direction must satisfy the inequality [86, 100, 116–118]
In the following three sections, we will discuss design space explorations for the three values of s obtained in Eqs. 18.17–18.19.
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