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Algorithms for Imprecise Tasks With 0/1-Constraints

We consider the problem of preemptively scheduling a set of imprecise computation tasks on a single processor, with the 0/1-constraint. In the imprecise computation model, each task consists of two parts, mandatory and optional, with the mandatory part required to be completed while the optional part can be left uncompleted. If a task has an optional part that is unfinished, then it incurs an error equal to the processing time of its unfinished potion. In the 0/1 constraint environment, each optional subtask is either fully scheduled or entirely discarded. Two performance metrics are considered: (1) the number of imprecisely scheduled tasks, (2) the total error. For the problem of minimizing the number of imprecisely scheduled tasks, it has been shown that it can be solved in O(n^3)-time. Since the time complexity is relatively high. We propose two O(n^2)-time algorithms for two special cases. On the other hand, it is known that the problem of minimizing the total error is NP-hard. We present an O(n^2) time algorithm to solve the problem when tasks have optional parts of the same length.