Online Non-Preemptive Scheduling to Minimize Maximum Weighted Flow-Time on Related Machines

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.

[1]  Denis Trystram,et al.  Online Non-Preemptive Scheduling in a Resource Augmentation Model Based on Duality , 2016, ESA.

[2]  Nikhil Bansal,et al.  Minimizing Maximum Flow-Time on Related Machines , 2016, Theory Comput..

[3]  Kirk Pruhs,et al.  Minimizing Maximum Flow Time on Related Machines via Dynamic Posted Pricing , 2017, ESA.

[4]  Benjamin Moseley,et al.  Online Scheduling to Minimize Maximum Response Time and Maximum Delay Factor , 2012, Theory Comput..

[5]  Amit Kumar,et al.  Minimizing Weighted lp-Norm of Flow-Time in the Rejection Model , 2015, FSTTCS.

[6]  Monaldo Mastrolilli,et al.  On-line scheduling to minimize max flow time: an optimal preemptive algorithm , 2005, Oper. Res. Lett..

[7]  Michael A. Bender,et al.  Flow and stretch metrics for scheduling continuous job streams , 1998, SODA '98.

[8]  Pierre-François Dutot,et al.  Online Non-preemptive Scheduling to Optimize Max Stretch on a Single Machine , 2016, COCOON.

[9]  Kirk Pruhs,et al.  Scheduling heterogeneous processors isn't as easy as you think , 2012, SODA.

[10]  Kyle Fox,et al.  Energy Efficient Scheduling of Parallelizable Jobs , 2013, SODA.

[11]  Amit Kumar,et al.  Resource augmentation for weighted flow-time explained by dual fitting , 2012, SODA.

[12]  Amit Kumar,et al.  Minimizing Maximum (Weighted) Flow-Time on Related and Unrelated Machines , 2015, Algorithmica.

[13]  Kirk Pruhs,et al.  Server Scheduling in the Weighted lp Norm , 2004, LATIN.

[14]  Bala Kalyanasundaram,et al.  Speed is as powerful as clairvoyance , 2000, JACM.

[15]  Nguyen Kim Thang,et al.  Lagrangian Duality in Online Scheduling with Resource Augmentation and Speed Scaling , 2013, ESA.

[16]  Cynthia A. Phillips,et al.  Optimal Time-Critical Scheduling via Resource Augmentation , 1997, STOC '97.

[17]  Amit Kumar,et al.  Rejecting jobs to minimize load and maximum flow-time , 2014, J. Comput. Syst. Sci..