A competitive algorithm for minimizing weighted flow time on unrelatedmachines with speed augmentation

We consider the online problem of scheduling jobs on unrelated machines so as to minimize the total weighted flow time. This problem has an unbounded competitive ratio even for very restricted settings. In this paper we show that if we allow the machines of the online algorithm to have ε more speed than those of the offline algorithm then we can get an O((1+ε-1)2)-competitive algorithm. Our algorithm schedules jobs preemptively but without migration. However, we compare our solution to an offline algorithm which allows migration. Our analysis uses a potential function argument which can also be extended to give a simpler and better proof of the randomized immediate dispatch algorithm of Chekuri-Goel-Khanna-Kumar for minimizing average flow time on parallel machines.

[1]  Kirk Pruhs,et al.  Non-Preemptive Min-Sum Scheduling with Resource Augmentation , 2007, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07).

[2]  Yossi Azar,et al.  Minimizing total flow time and total completion time with immediate dispatching , 2003, SPAA.

[3]  V. N. Muralidhara,et al.  Minimizing Total Flow-Time: The Unrelated Case , 2008, ISAAC.

[4]  Sanjeev Khanna,et al.  Algorithms for minimizing weighted flow time , 2001, STOC '01.

[5]  Luca Becchetti,et al.  Nonclairvoyant scheduling to minimize the total flow time on single and parallel machines , 2004, JACM.

[6]  Ashish Goel,et al.  Multi-processor scheduling to minimize flow time with ε resource augmentation , 2004, STOC '04.

[7]  Rajeev Motwani,et al.  Non-clairvoyant scheduling , 1994, SODA '93.

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

[9]  Amit Kumar,et al.  Minimizing Average Flow-time : Upper and Lower Bounds , 2007, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07).

[10]  Amit Kumar,et al.  Minimizing average flow time on related machines , 2006, STOC '06.

[11]  Kirk Pruhs,et al.  Server scheduling in the Lp norm: a rising tide lifts all boat , 2003, STOC '03.

[12]  Amit Kumar,et al.  Better Algorithms for Minimizing Average Flow-Time on Related Machines , 2006, ICALP.

[13]  Bala Kalyanasundaram,et al.  Speed is as powerful as clairvoyance [scheduling problems] , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[14]  Gerhard J. Woeginger,et al.  Approximability and nonapproximability results for minimizing total flow time on a single machine , 1996, STOC '96.

[15]  Yossi Azar,et al.  Minimizing the flow time without migration , 1999, STOC '99.

[16]  Gerhard J. Woeginger,et al.  Approximability and Nonapproximability Results for Minimizing Total Flow Time on a Single Machine , 1999, SIAM J. Comput..

[17]  Stefano Leonardi,et al.  Approximating total flow time on parallel machines , 2007, J. Comput. Syst. Sci..