It is well known that the optimal nonpreemptive scheduling of n tasks on a single processor requires a number of operations proportional to the factorial of the number of tasks. It is proposed that tasks be scheduled in two steps. In the first step a sequence for the tasks is generated, and in the second step the tasks are bounded in time according to the selected sequence by assigning a start time for each task. In the general case the proposed decomposition scheduling scheme divides the n tasks into m subsets, and the tasks are scheduled within each subset. The complexity of the approach is determined when the tasks in a subset are scheduled using exhaustive search procedures.
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