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<p><b>Abstract</b>—Loop scheduling is an important problem in parallel processing. The retiming technique reorganizes an iteration; the unfolding technique schedules several iterations together. We combine these two techniques to obtain a static schedule with a reduced average computation time per iteration. We first prove that the order of retiming and unfolding is immaterial for scheduling a data-flow graph (DFG). From this nice property, we present a polynomial-time algorithm on the original DFG, before unfolding, to find the minimum-rate static schedule for a given unfolding factor. For the case of a unit-time DFG, efficient checking and retiming algorithms are presented.</p>
Data-flow graphs, loop parallelization, parallel processing, retiming, scheduling, unfolding.

E. H. Sha and L. Chao, "Scheduling Data-Flow Graphs via Retiming and Unfolding," in IEEE Transactions on Parallel & Distributed Systems, vol. 8, no. , pp. 1259-1267, 1997.
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