Online Non-Preemptive Scheduling to Minimize Maximum Weighted Flow-Time on Related Machines
Giorgio Lucarelli, Benjamin Moseley, Thang, Nguyen Kim, Abhinav Srivastav, Denis Trystram · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2019
We consider the problem of scheduling jobs to minimize the maximum weighted flow-time on a set of related machines. When jobs can be preempted this problem is well-understood; for example, there exists a constant competitive algorithm using speed augmentation. When jobs must be scheduled non-preemptively, only hardness results are known. In this paper, we present the first online guarantees for the non-preemptive variant. We present the first constant competitive algorithm for minimizing the maximum weighted flow-time on related machines by relaxing the problem and assuming that the online algorithm can reject a small fraction of the total weight of jobs. This is essentially the best result possible given the strong lower bounds on the non-preemptive problem without rejection.