Little-Preemptive Scheduling on Unrelated Processors.

Abstract

We consider the preemptive scheduling of n independent jobs on m unrelated machines to minimize the makespan. Preemptive schedules with at most 2m−3 preemptions are built, which are optimal when the maximal job processing time is no more than the optimal schedule makespan. We further restrict the maximal job processing time and obtain optimal schedules with at most m−1 preemptions. This is better than the earlier known best bound of 4m2−5m+2 on the total number of preemptions. Without the restriction on the maximal job processing time, our (2m−3)-preemptive schedules have a makespan which is no more than either of the following two magnitudes: (a) the maximum between the longest job processing time and the optimal preemptive makespan, and (b) the optimal nonpreemptive makespan. Our (m−1)-preemptive schedules might be at most twice worse than an optimal one.