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.
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