Scheduling imprecise computation tasks on uniform processors

We consider the problem of preemptively scheduling n imprecise computation tasks on m⩾1 uniform processors, with each task Ti having two weights wi and . Three objectives are considered: (1) minimizing the maximum w′-weighted error; (2) minimizing the total w-weighted error subject to the constraint that the maximum w′-weighted error is minimized; (3) minimizing the maximum w′-weighted error subject to the constraint that the total w-weighted error is minimized. For these objectives, we give polynomial time algorithms with time complexity O(mn4), O(mn4) and O(kmn4), respectively, where k is the number of distinct w-weights. We also present alternative algorithms for the three objectives, with time complexity O(cmn3), O(cmn3+mn4) and O(kcmn3), respectively, where c is a parameter-dependent number.