Time optimal linear schedules for algorithms with uniform dependencies

The problem of identifying the time-optimal linear schedules for uniform dependence algorithms with any convex-polyhedron index set is addressed. Optimization procedures are proposed, and the class of algorithms is identified for which the total execution times by the optimal linear schedule and the free schedule that schedules the computation to execute as soon as its operands are available are equal. This method is useful in mapping algorithms onto systolic/MIMD (multiple-instruction, multiple-instruction stream) systems.<>