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Speed Scaling of Tasks with Precedence Constraints

  • Conference paper
Approximation and Online Algorithms (WAOA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3879))

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Abstract

We consider the problem of speed scaling to conserve energy in a multiprocessor setting where there are precedence constraints between tasks, and where the performance measure is the makespan. That is, we consider an energy bounded version of the classic problem Pm | prec | C max . We show that, without loss of generality, one need only consider constant power schedules. We then show how to reduce this problem to the problem Qm | prec | C max to obtain a poly-log(m)-approximation algorithm.

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References

  1. Alon, N., Azar, Y., Woeginger, G., Yadid, T.: Approximation schemes for scheduling. In: ACM-SIAM Symposium on Discrete Algorithms, pp. 493–500 (1997)

    Google Scholar 

  2. Bansal, N., Kimbrel, T., Pruhs, K.: Dynamic speed scaling to manage energy and temperature. In: IEEE Syposium on Foundations of Computer Science, pp. 520–529 (2004)

    Google Scholar 

  3. Bansal, N., Pruhs, K.: Speed scaling to manage temperature. In: Symposium on Theoretical Aspects of Computer Science, pp. 460–471 (2005)

    Google Scholar 

  4. 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)

    Article  Google Scholar 

  5. Chekuri, C., Bender, M.A.: An efficient approximation algorithm for minimizing makespan on uniformly related machines. Journal of Algorithms 41, 212–224 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chen, J.-J., Kuo, T.-W., Lu, H.-I.: Power-saving scheduling for weakly dynamic voltage scaling devices. In: Dehne, F., López-Ortiz, A., Sack, J.-R. (eds.) WADS 2005. LNCS, vol. 3608, pp. 338–349. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  7. Chudak, F.A., Shmoys, D.B.: Approximation algorithms for precedence-constrained scheduling problems on parallel machines that run at different speeds. In: ACM-SIAM Symposium on Discrete Algorithms, pp. 581–590 (1997)

    Google Scholar 

  8. Graham, R.L.: Bounds for certain multiprocessor anomalies. Bell System Techical Journal 45, 1563–1581 (1966)

    Article  MATH  Google Scholar 

  9. Graham, R.L., Lawler, E., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic scheduling: A survey. Annals of Discrete Mathematics 5, 287–326 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  10. Gruian, F., Kuchcinski, K.: Lenes: Task-scheduling for low-energy systems using variable voltage processors. In: Asia South Pacific - Design Automation Conference, pp. 449–455 (2001)

    Google Scholar 

  11. Irani, S., Pruhs, K.: Algorithmic problems in power management. In: SIGACT News (2005)

    Google Scholar 

  12. Kwon, W.-C., Kim, T.: Optimal voltage allocation techniques for dynamically variable voltage processors. ACM Transactions on Embedded Computing Systems (TECS) 4(1), 211–230 (2005)

    Article  Google Scholar 

  13. Li, M., Liu, B.J., Yao, F.F.: Min-energy voltage allocation for tree-structured tasks. In: Wang, L. (ed.) COCOON 2005. LNCS, vol. 3595, pp. 283–296. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  14. Luo, J., Jha, N.K.: Power-conscious joint scheduling of periodic task graphs and aperiodic task graphs in distributed real-time embedded systems. In: International Conference on Computer Aided Design, pp. 357–364 (2000)

    Google Scholar 

  15. Mishra, R., Rastogi, N., Zhu, D., Moss, D., Melhem, R.G.: Energy aware scheduling for distributed real-time systems. In: International Parallel and Distributed Processing Symposium, p. 21 (2003)

    Google Scholar 

  16. Mudge, T.: Power: A first-class architectural design constraint. Computer 34(4), 52–58 (2001)

    Article  Google Scholar 

  17. Pruhs, K., Uthaisombut, P., Woeginger, G.: Getting the best response for your erg. In: Hagerup, T., Katajainen, J. (eds.) SWAT 2004. LNCS, vol. 3111, pp. 14–25. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  18. Frances Yao, F., Demers, A.J., Shenker, S.: A scheduling model for reduced cpu energy. In: IEEE Syposium on Foundations of Computer Science (FOCS 1995), pp. 374–382 (1995)

    Google Scholar 

  19. Yun, H.-S., Kim, J.: On energy-optimal voltage scheduling for fixed priority hard real-time systems. ACM Transactions on Embedded Computing Systems 2(3), 393–430 (2003)

    Article  Google Scholar 

  20. Zhang, Y., Hu, X., Chen, D.Z.: Task scheduling and voltage selection for energy minimization. In: Design Automation Conference, pp. 183–188 (2002)

    Google Scholar 

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Pruhs, K., van Stee, R., Uthaisombut, P. (2006). Speed Scaling of Tasks with Precedence Constraints. In: Erlebach, T., Persinao, G. (eds) Approximation and Online Algorithms. WAOA 2005. Lecture Notes in Computer Science, vol 3879. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11671411_24

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  • DOI: https://doi.org/10.1007/11671411_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32207-8

  • Online ISBN: 978-3-540-32208-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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