Time optimal linear schedules for algorithms with uniform dependencies

The authors address the problem of identifying optimal linear schedules for uniform dependence algorithms so that their execution time is minimized. Procedures are proposed to solve this problem based on the mathematical solution of a nonlinear optimization problem. The complexity of these procedures is independent of the size of the algorithm. Actually, the complexity is exponential in the dimension of the index set of the algorithm, and for all practical purposes, very small due to the limited dimension of the index set of algorithms of practical interest. A particular class of algorithms for which the proposed solution is greatly simplified is considered, and the corresponding simpler organization procedure is provided.<
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