Abstract
We consider the problem of unrelated parallel machine scheduling when the DVS (dynamic voltage scaling) method is used to conserve energy consumption. Given an energy budget, we present (2 + ε)-approximation algorithms for the makespan minimization problem under two different settings, the continuous model in which speeds are allowed to be any real number in [s min ,s max ] and the discrete model in which only d distinct speeds are available. We also show how to derive a 2-approximation algorithm if the energy budget is allowed to be slightly exceeded.
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References
Albers, S., Muller, F., Schmelzer, S.: Speed scaling on parallel processors. In: Proceedings of the 19th Annual ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 289–298 (2007)
Alon, N., Azar, Y., Woeginger, G.J., Yadid, T.: Approximation schemes for scheduling on parallel machines. Journal of Scheduling 1, 55–66 (1998)
Grigoriev, A., Sviridenko, M., Uetz, M.: Machine scheduling with resource dependent processing times. Mathematical Programming 110(1), 209–228 (2007)
Kwon, W.C., Kim, T.: Optimal voltage allocation techniques for dynamically variable voltage processors. ACM Transactions on Embedded Computing Systems 4(1), 211–230 (2005)
Lenstra, J.K., Shmoys, D.B., Tardos, E.: Approximation algorithms for scheduling unrelated parallel machines. Mathematical Programming 46, 259–271 (1990)
Phillips, C., Stein, C., Wein, J.: Task scheduling in networks. In: Schmidt, E.M., Skyum, S. (eds.) SWAT 1994. LNCS, vol. 824, pp. 290–301. Springer, Heidelberg (1994)
Pruhs, K., van Stee, R., Uthaisombut, P.: Speed scaling of tasks with precedence constraints. Theory of Computing Systems 43(1), 67–80 (2008)
Shchepin, E.V., Vakhania, N.: An optimal rounding gives a better approximation for scheduling unrelated machines. Operations Research Letters 33(2), 127–133 (2005)
Yao, F., Demers, A., Shenker, S.: A scheduling model for reduced CPU energy. In: Proceedings of the 36th Annual Symposium on Foundations of Computer Science (FOCS), pp. 374–382 (1995)
Yao, F., Li, M.: An efficient algorithm for computing optimal discrete voltage schedules. SIAM Journal on Computing 35(3), 658–671 (2006)
Yu, L., Shih, H., Pfund, M.E., Carlyle, W.M., Fowler, J.W.: Scheduling of unrelated parallel-machines: An application to PWB manufacturing. IIE Transactions on Scheduling and Logistics 34, 921–931 (2002)
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Chen, L., Luo, W., Zhang, G. (2011). Approximation Algorithms for Unrelated Machine Scheduling with an Energy Budget. In: Atallah, M., Li, XY., Zhu, B. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 6681. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21204-8_27
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DOI: https://doi.org/10.1007/978-3-642-21204-8_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21203-1
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