Fast algorithms for scheduling imprecise computations

Consideration is given to the problem of scheduling tasks each of which is logically decomposed into a mandatory subtask and an optional subtask. The mandatory subtask must be executed to completion. If the available processor time is insufficient, the optional subtask can be left incomplete. The error in the result of a task is equal to the processing time of the unfinished portion of the optional subtask. A description is given of a preemptive algorithm for scheduling n dependent tasks with rational ready times, deadlines, and processing times on a uniprocessor system. This algorithm determines whether feasible schedules that meet the timing constraints of all tasks exist; when feasible schedules exist, it finds one that has the minimum total error. The complexity of this algorithm is O(n log n). A schedule is said to satisfy the 0/1 constraint when every optional subtask is either completed or discarded. The problem of finding an optimal feasible schedule that satisfies the 0/1 constraint and minimizes the number of discarded optional subtasks is NP-complete. Two algorithms are presented for finding optimal schedules of dependent tasks on a uniprocessor system for the special case when all optional subtasks have identical processing times