Online Non-preemptive Scheduling to Minimize Maximum Weighted Flow-time on Related Machines
Résumé
We consider the problem of scheduling jobs to minimize the maximum weighted flow-timeon a set of related machines. When jobs can be preempted this problem is well-understood; forexample, there exists a constant competitive algorithm using speed augmentation. When jobs mustbe scheduled non-preemptively, only hardness results are known. In this paper, we present thefirst online guarantees for the non-preemptive variant. We present the first constant competitivealgorithm for minimizing the maximum weighted flow-time on related machines by relaxing theproblem and assuming that the online algorithm can reject a small fraction of the total weight ofjobs. This is essentially the best result possible given the strong lower bounds on the non-preemptiveproblem without rejection.