Scheduling on Power-Heterogeneous Processors

  • Susanne Albers
  • Evripidis Bampis
  • Dimitrios Letsios
  • Giorgio Lucarelli
  • Richard Stotz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9644)

Abstract

We consider the problem of scheduling a set of jobs, each one specified by its release date, its deadline and its processing volume, on a set of heterogeneous speed-scalable processors, where the energy-consumption rate is processor-dependent. Our objective is to minimize the total energy consumption when both the preemption and the migration of jobs are allowed. We propose a new algorithm based on a compact linear programming formulation. Our method approaches the value of the optimal solution within any desired accuracy for a large set of continuous power functions. Furthermore, we develop a faster combinatorial algorithm based on flows for standard power functions and jobs whose density is lower bounded by a small constant. Finally, we extend and analyze the AVerage Rate (AVR) online algorithm in the heterogeneous setting.

References

  1. 1.
    Albers, S., Antoniadis, A., Greiner, G.: On multi-processor speed scaling with migration. J. Comput. Syst. Sci. 81(7), 1194–1209 (2015)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Angel, E., Bampis, E., Kacem, F., Letsios, D.: Speed scaling on parallel processors with migration. In: Kaklamanis, C., Papatheodorou, T., Spirakis, P.G. (eds.) Euro-Par 2012. LNCS, vol. 7484, pp. 128–140. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  3. 3.
    Bampis, E., Kononov, A.V., Letsios, D., Lucarelli, G., Sviridenko, M.: Energy efficient scheduling and routing via randomized rounding. In: FSTTCS, vol. 24 of LIPIcs, pp. 449–460. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2013)Google Scholar
  4. 4.
    Bampis, E., Letsios, D., Lucarelli, G.: Green scheduling, flows and matchings. Theor. Comput. Sci. 579, 126–136 (2015)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Bansal, N., Bunde, D.P., Chan, H.-L., Pruhs, K.: Average rate speed scaling. Algorithmica 60(4), 877–889 (2011)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Bansal, N., Chan, H.-L., Pruhs, K.: Speed scaling with an arbitrary power function. ACM Trans. Algorithms 9(2), 18 (2013)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Bansal, N., Kimbrel, T., Pruhs, K.: Speed scaling to manage energy and temperature. J. ACM 54(1) (2007)Google Scholar
  8. 8.
    Bingham, B.D., Greenstreet, M.R.: Energy optimal scheduling on multiprocessors with migration. In: ISPA, pp. 153–161 (2008)Google Scholar
  9. 9.
    Chen, J.-J., Hsu, H.-R., Chuang, K.-H., Yang, C.-L., Pang, A.-C., Kuo, T.-W.: Multiprocessor energy-efficient scheduling with task migration considerations. In: ECRTS, pp. 101–108. IEEE Computer Society (2004)Google Scholar
  10. 10.
    Federgruen, A., Groenevelt, H.: Preemptive scheduling of uniform machines by ordinary network flow techniques. Manage. Sci. 32(3), 341–349 (1986)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Gonzalez, T., Sahni, S.: Open shop scheduling to minimize finish time. J. ACM 23(4), 665–679 (1976)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Gonzalez, T., Sahni, S.: Preemptive scheduling of uniform processor systems. J. ACM 25, 92–101 (1978)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Gupta, A., Im, S., Krishnaswamy, R., Moseley, B., Pruhs, K.: Scheduling heterogeneous processors isn’t as easy as you think. In: SODA, pp. 1242–1253 (2012)Google Scholar
  14. 14.
    Gupta, A., Krishnaswamy, R., Pruhs, K.: Scalably scheduling power-heterogeneous processors. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6198, pp. 312–323. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  15. 15.
    Li, M., Yao, A.C., Yao, F.F.: Discrete and continuous min-energy schedules for variable voltage processors. PNAS 103(11), 3983–3987 (2006)CrossRefGoogle Scholar
  16. 16.
    Yao, F., Demers, A., Shenker, S.: A scheduling model for reduced CPU energy. In: FOCS, pp. 374–382 (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Susanne Albers
    • 1
  • Evripidis Bampis
    • 2
  • Dimitrios Letsios
    • 3
  • Giorgio Lucarelli
    • 4
  • Richard Stotz
    • 1
  1. 1.Fakultät für InformatikTechnische Universität MünchenMunichGermany
  2. 2.Sorbonne Universités, UPMC Univ. Paris 06, UMR 7606, LIP6ParisFrance
  3. 3.Univ. Nice Sophia Antipolis, CNRS, I3S, UMR 7271Sophia AntipolisFrance
  4. 4.Université Grenoble-Alpes, INP, UMR 5217, LIGSaint-Martin-d’HèresFrance

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