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<p>This paper describes several loop transformation techniques for extracting parallelism from nested loop structures. Nested loops can then be scheduled to run in parallel so thatexecution time is minimized. One technique is called selective cycle shrinking, and theother is called true dependence cycle shrinking. It is shown how selective shrinking isrelated to linear scheduling of nested loops and how true dependence shrinking is relatedto conflict-free mappings of higher dimensional algorithms into lower dimensionalprocessor arrays. Methods are proposed in this paper to find the selective and truedependence shrinkings with minimum total execution time by applying the techniques offinding optimal linear schedules and optimal and conflict-free mappings proposed by W.Shang and A.B. Fortes.</p>
Index Termsscheduling; program compilers; loop transformations; generalized cycle shrinking;parallelism; nested loop structures; selective cycle shrinking; linear scheduling;conflict-free mappings

J. Fortes, M. O'Keefe and W. Shang, "On Loop Transformations for Generalized Cycle Shrinking," in IEEE Transactions on Parallel & Distributed Systems, vol. 5, no. , pp. 193-204, 1994.
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