Abstract
In this paper we study energy efficient deadline scheduling on multiprocessors in which the processors consumes power at a rate of s α when running at speed s, where α ≥ 2. The problem is to dispatch jobs to processors and determine the speed and jobs to run for each processor so as to complete all jobs by their deadlines using the minimum energy. The problem has been well studied for the single processor case. For the multiprocessor setting, constant competitive online algorithms for special cases of unit size jobs or arbitrary size jobs with agreeable deadlines have been proposed [4]. A randomized algorithm has been proposed for jobs of arbitrary sizes and arbitrary deadlines [13]. We propose a deterministic online algorithm for the general setting and show that it is O(logα P)-competitive, where P is the ratio of the maximum and minimum job size.
This work is partially supported by EPSRC Grant EP/E028276/1.
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References
Albers, S.: Algorithms for energy saving. In: Albers, S., Alt, H., Näher, S. (eds.) Efficient Algorithms. LNCS, vol. 5760, pp. 173–186. Springer, Heidelberg (2009)
Albers, S.: Energy-efficient algorithms. Communication ACM 53(5), 86–96 (2010)
Albers, S., Fujiwara, H.: Energy-efficient algorithms for flow time minimization. ACM Transactions on Algorithms 3(4), 49 (2007)
Albers, S., Muller, F., Schmelzer, S.: Speed scaling on parallel processors. In: Proceedings of ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 289–298 (2007)
Bansal, N., Chan, H.L., Lam, T.W., Lee, L.K.: Scheduling for speed bounded processors. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 409–420. Springer, Heidelberg (2008)
Bansal, N., Chan, H.L., Pruhs, K.: Speed scaling with an arbitrary power function. In: Proceedings of ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 693–701 (2009)
Bansal, N., Chan, H.L., Pruhs, K., Rogozhnikov-Katz, D.: Improved bounds for speed scaling in devices obeying the cube-root rule. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5555, pp. 144–155. Springer, Heidelberg (2009)
Bansal, N., Kimbrel, T., Pruhs, K.: Speed scaling to manage energy and temperature. Journal of the ACM 54(1), 3 (2007)
Bansal, N., Pruhs, K., Stein, C.: Speed scaling for weighted flow time. In: Proceedings of ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 805–813 (2007)
Becker, H.W., Riordan, J.: The arithmetic of Bell and Stirling numbers. American Journal of Mathematics 70, 385–394 (1948)
Brooks, D.M., Bose, P., Schuster, S.E., Jacobson, H., Kudva, P.N., Buyuktosunoglu, A., Wellman, J.D., Zyuban, V., Gupta, M., Cook, P.W.: Power-aware microarchitecture: Design and modeling challenges for next-generation microprocessors. IEEE Micro 20(6), 26–44 (2000)
Chan, H.L., Chan, W.T., Lam, T.W., Lee, L.K., Mak, K.S., Wong, P.W.H.: Optimizing throughput and energy in online deadline scheduling. ACM Transactions on Algorithms 6(1), 10 (2009); Preliminary version appeared in Proceedings of Symposium on Discrete Algorithms SODA, pp. 795–804 (2007)
Greiner, G., Nonner, T., Souza, A.: The bell is ringing in speed-scaled multiprocessor scheduling. In: Proceedings of ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 11–18 (2009)
Han, X., Lam, T.-W., Lee, L.-K., To, I.K.-K., Wong, P.W.-H.: Deadline scheduling and power management for speed bounded processors. Theoretical Computer Science 411(40-42), 3587–3600 (2010)
Irani, S., Pruhs, K.: Algorithmic problems in power management. ACM SIGACT News 32(2), 63–76 (2005)
Irani, S., Shukla, S., Gupta, R.K.: Algorithms for power savings. ACM Transactions on Algorithms 3(4), 41 (2007)
Lam, T.W., Lee, L.K., Ting, H.F., To, I.K.K., Wong, P.W.H.: Sleep with guilt and work faster to minimize flow plus energy. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5555, pp. 665–676. Springer, Heidelberg (2009)
Lam, T.W., Lee, L.K., To, I.K.K., Wong, P.W.H.: Improved multi-processor scheduling for flow time and energy. Journal of Scheduling (to appear), http://dx.doi.org/10.1016/j.tcs.2010.05.035 ; Preliminary version appeared in Proceedings of ACM Symposium on Parallelism in Algorithms and Architectures, pp. 256–264 (2008)
Lam, T.W., Lee, L.K., To, I.K.K., Wong, P.W.H.: Speed scaling functions for flow time scheduling based on active job count. In: Halperin, D., Mehlhorn, K. (eds.) ESA 2008. LNCS, vol. 5193, pp. 647–659. Springer, Heidelberg (2008)
Mudge, T.: Power: A first-class architectural design constraint. Computer 34(4), 52–58 (2001)
Yao, F., Demers, A., Shenker, S.: A scheduling model for reduced CPU energy. In: Proceedings of IEEE Symposium on Foundations of Computer Science (FOCS), pp. 374–382 (1995)
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Bell, P.C., Wong, P.W.H. (2011). Multiprocessor Speed Scaling for Jobs with Arbitrary Sizes and Deadlines. In: Ogihara, M., Tarui, J. (eds) Theory and Applications of Models of Computation. TAMC 2011. Lecture Notes in Computer Science, vol 6648. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20877-5_4
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DOI: https://doi.org/10.1007/978-3-642-20877-5_4
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