ABSTRACT
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.
- S. Anand, Naveen Garg, and Amit Kumar. An O(log P) competitive algorithm for minimizing flow time on related machines. Unpublished manuscript, 2009.Google Scholar
- Nir Avrahami and Yossi Azar. Minimizing total flow time and total completion time with immediate dispatching. Algorithmica, 47(3):253--268, 2007. Google ScholarDigital Library
- Baruch Awerbuch, Yossi Azar, Stefano Leonardi, and Oded Regev. Minimizing the flow time without migration. In ACM Symposium on Theory of Computing, pages 198--205, 1999. Google ScholarDigital Library
- Baruch Awerbuch, Yossi Azar, Stefano Leonardi, and Oded Regev. Minimizing the flow time without migration. SIAM J. Comput., 31(5):1370--1382, 2002. Google ScholarDigital Library
- N. Bansal and K. Pruhs. Server scheduling in the Lp norm: A rising tide lifts all boats. In ACM Symposium on Theory of Computing, pages 242--250, 2003. Google ScholarDigital Library
- Nikhil Bansal, Ho-Leung Chan, Rohit Khandekar, Kirk Pruhs, Clifford Stein, and Baruch Schieber. Non-preemptive min-sum scheduling with resource augmentation. In IEEE Symposium on Foundations of Computer Science, pages 614--624, 2007. Google ScholarDigital Library
- Luca Becchetti and Stefano Leonardi. Nonclairvoyant scheduling to minimize the total flow time on single and parallel machines. J. ACM, 51(4):517--539, 2004. Google ScholarDigital Library
- C. Chekuri, S. Khanna, and A. Zhu. Algorithms for weighted flow time. In ACM Symposium on Theory of Computing, pages 84--93. ACM, 2001. Google ScholarDigital Library
- Chandra Chekuri, Ashish Goel, Sanjeev Khanna, and Amit Kumar. Multi-processor scheduling to minimize flow time with epsilon resource augmentation. In ACM Symposium on Theory of Computing, pages 363--372, 2004. Google ScholarDigital Library
- Naveen Garg and Amit Kumar. Better algorithms for minimizing average flow-time on related machines. In ICALP (1), pages 181--190, 2006. Google ScholarDigital Library
- Naveen Garg and Amit Kumar. Minimizing average flow time on related machines. In ACM Symposium on Theory of Computing, pages 730--738, 2006. Google ScholarDigital Library
- Naveen Garg and Amit Kumar. Minimizing average flow-time : Upper and lower bounds. In IEEE Symposium on Foundations of Computer Science, pages 603--613, 2007. Google ScholarDigital Library
- Naveen Garg, Amit Kumar, and Muralidhara V N. Minimizing total flow-time: The unrelated case. In ISAAC, pages 424--435, 2008. Google ScholarDigital Library
- Bala Kalyanasundaram and Kirk Pruhs. Speed is as powerful as clairvoyance. In IEEE Symposium on Foundations of Computer Science, pages 214--221, 1995. Google ScholarDigital Library
- Hans Kellerer, Thomas Tautenhahn, and Gerhard J. Woeginger. Approximability and nonapproximability results for minimizing total flow time on a single machine. In ACM Symposium on Theory of Computing, pages 418--426, 1996. Google ScholarDigital Library
- Stefano Leonardi and Danny Raz. Approximating total flow time on parallel machines. In ACM Symposium on Theory of Computing, pages 110--119, 1997. Google ScholarDigital Library
- R. Motwani, S. Phillips, and E. Torng. Non-clairvoyant scheduling. Theoretical Computer Science, 130(1):17--47, 1994. Google ScholarDigital Library
Index Terms
- A competitive algorithm for minimizing weighted flow time on unrelatedmachines with speed augmentation
Recommendations
Minimizing weighted flow time
We consider the problem of minimizing the total weighted flow time on a single machine with preemptions. We give an online algorithm that is O(k)-competitive for k weight classes. This implies an O(log W)-competitive algorithm, where W is the maximum to ...
Minimizing average flow time on related machines
STOC '06: Proceedings of the thirty-eighth annual ACM symposium on Theory of ComputingWe give the first on-line poly-logarithmic competitve algorithm for minimizing average flow time with preemption on related machines, i.e., when machines can have different speeds. This also yields the first poly-logarithmic polynomial time ...
Minimizing Flow-Time on Unrelated Machines
STOC '15: Proceedings of the forty-seventh annual ACM symposium on Theory of ComputingWe consider some classical flow-time minimization problems in the unrelated machines setting. In this setting, there is a set of m machines and a set of n jobs, and each job j has a machine dependent processing time of pij on machine i. The flow-time of ...
Comments