A reindexing based approach towards mapping of DAG with affine schedules onto parallel embedded systems

We address the problem of optimally mapping uniform DAGs to systolic arrays, given an affine timing function. We introduce an automatic allocation method based on a preprocessing by reindexing that transforms the initial DAG into a new one that enables the well known projection method to minimize the number of processors along a number of directions. We demonstrate its superiority to other methods, and establish the space-optimality of the proposed method. We also show an upper bound on the number of processors that corresponds to the best space complexity that both the projection method, and the so-called grouping method can give for the initial DAG. We also describe how the new allocation method can be implemented in tools.