Scheduling imprecise computation tasks on uniform processors

Abstract

We consider the problem of preemptively scheduling n imprecise computation tasks on m ⩾ 1 uniform processors, with each task T i having two weights w i and w i ′ . 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 ( m n 4 ) , O ( m n 4 ) and O ( k m n 4 ) , respectively, where k is the number of distinct w-weights. We also present alternative algorithms for the three objectives, with time complexity O ( c m n 3 ) , O ( c m n 3 + m n 4 ) and O ( k c m n 3 ) , respectively, where c is a parameter-dependent number.