Speed-Scaling with No Preemptions

  • Evripidis Bampis
  • Dimitrios Letsios
  • Giorgio Lucarelli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8889)

Abstract

We revisit the non-preemptive speed-scaling problem, in which a set of jobs have to be executed on a single or a set of parallel speed-scalable processor(s) between their release dates and deadlines so that the energy consumption to be minimized. We adopt the speed-scaling mechanism first introduced in [Yao et al., FOCS 1995] according to which the power dissipated is a convex function of the processor’s speed. Intuitively, the higher is the speed of a processor, the higher is the energy consumption. For the single-processor case, we improve the best known approximation algorithm by providing a \((1+\epsilon )^{\alpha }\tilde{B}_{\alpha }\)-approximation algorithm, where \(\tilde{B}_{\alpha }\) is a generalization of the Bell number. For the multiprocessor case, we present an approximation algorithm of ratio \(\tilde{B}_{\alpha }((1+\epsilon )(1+\frac{w_{\max }}{w_{\min }}))^{\alpha }\) improving the best known result by a factor of \((\frac{5}{2})^{\alpha -1}(\frac{w_{\max }}{w_{\min }})^{\alpha }\). Notice that our result holds for the fully heterogeneous environment while the previous known result holds only in the more restricted case of parallel processors with identical power functions.

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References

  1. 1.
    Albers, S.: Energy-efficient algorithms. Communications of the ACM 53(5), 86–96 (2010)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Albers, S.: Algorithms for dynamic speed scaling. In: STACS. LIPIcs, vol. 9, pp. 1–11. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2011)Google Scholar
  3. 3.
    Albers, S., Antoniadis, A., Greiner, G.: On multi-processor speed scaling with migration: extended abstract. In: SPAA, pp. 279–288. ACM (2011)Google Scholar
  4. 4.
    Albers, S., Müller, F., Schmelzer, S.: Speed scaling on parallel processors. In: SPAA, pp. 289–298. ACM (2007)Google Scholar
  5. 5.
    Angel, E., Bampis, E., Chau, V.: Throughput maximization in the speed-scaling setting. CoRR, abs/1309.1732 (2013)Google Scholar
  6. 6.
    Angel, Eric, Bampis, Evripidis, Kacem, Fadi, Letsios, Dimitrios: Speed Scaling on Parallel Processors with Migration. In: Kaklamanis, Christos, Papatheodorou, Theodore, Spirakis, Paul G. (eds.) Euro-Par 2012. LNCS, vol. 7484, pp. 128–140. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  7. 7.
    Antoniadis, Antonios, Huang, Chien-Chung: Non-preemptive Speed Scaling. In: Fomin, Fedor V., Kaski, Petteri (eds.) SWAT 2012. LNCS, vol. 7357, pp. 249–260. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  8. 8.
    Bampis, Evripidis, Kononov, Alexander, Letsios, Dimitrios, Lucarelli, Giorgio, Nemparis, Ioannis: From Preemptive to Non-preemptive Speed-Scaling Scheduling. In: Du, Ding-Zhu, Zhang, Guochuan (eds.) COCOON 2013. LNCS, vol. 7936, pp. 134–146. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  9. 9.
    Bampis, E., Kononov, A., Letsios, D., Lucarelli, G., Sviridenko, M.: Energy efficient scheduling and routing via randomized rounding. In: FSTTCS. LIPIcs, vol. 24, pp. 449–460. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2013)Google Scholar
  10. 10.
    Bampis, Evripidis, Letsios, Dimitrios, Lucarelli, Giorgio: Green Scheduling, Flows and Matchings. In: Chao, Kun-Mao, Hsu, Tsan-sheng, Lee, Der-Tsai (eds.) ISAAC 2012. LNCS, vol. 7676, pp. 106–115. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  11. 11.
    Bampis, Evripidis, Letsios, Dimitrios, Milis, Ioannis, Zois, Georgios: Speed Scaling for Maximum Lateness. In: Gudmundsson, Joachim, Mestre, Julián, Viglas, Taso (eds.) COCOON 2012. LNCS, vol. 7434, pp. 25–36. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  12. 12.
    Bingham, B.D., Greenstreet, M.R.: Energy optimal scheduling on multiprocessors with migration. In: ISPA, pp. 153–161. IEEE (2008)Google Scholar
  13. 13.
    Bunde, D.P.: Power-aware scheduling for makespan and flow. In: SPAA, pp. 190–196. ACM (2006)Google Scholar
  14. 14.
    Chan, H.-L., Chan, W.-T., Lam, T. W., Lee, L.-K., Mak, K.-S., Wong, P. W. H.: Energy efficient online deadline scheduling. In: SODA, pp. 795–804 (2007)Google Scholar
  15. 15.
    Cohen-Addad, V., Li, Z., Mathieu, C., Milis, I.: Energy-efficient algorithms for non-preemptive speed-scaling. In: WAOA. LNCS. Springer (2014)Google Scholar
  16. 16.
    Greiner, G., Nonner, T., Souza, A.: The bell is ringing in speed-scaled multiprocessor scheduling. In: SPAA, pp. 11–18. ACM (2009)Google Scholar
  17. 17.
    Hochbaum, D.S., Shmoys, D.B.: Using dual approximation algorithms for scheduling problems: Theoretical and practical results. Journal of the ACM 34, 144–162 (1987)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Huang, Chien-Chung, Ott, Sebastian: New Results for Non-Preemptive Speed Scaling. In: Csuhaj-Varjú, Erzsébet, Dietzfelbinger, Martin, Ésik, Zoltán (eds.) MFCS 2014, Part II. LNCS, vol. 8635, pp. 360–371. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  19. 19.
    Li, M., Yao, F.F.: An efficient algorithm for computing optimal discrete voltage schedules. SIAM Journal on Computing 35, 658–671 (2006)CrossRefMATHMathSciNetGoogle Scholar
  20. 20.
    Pruhs, K., van Stee, R., Uthaisombut, P.: Speed scaling of tasks with precedence constraints. Theory of Computing Systems 43, 67–80 (2008)CrossRefMATHMathSciNetGoogle Scholar
  21. 21.
    Wierman, A., Andrew, L.L.H., Tang, A.: Power-aware speed scaling in processor sharing systems. In: INFOCOM, pp. 2007–2015. IEEE (2009)Google Scholar
  22. 22.
    Yao, F.F., Demers, A.J., Shenker, S.: A scheduling model for reduced CPU energy. In: FOCS, pp. 374–382. IEEE Computer Society (1995)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Evripidis Bampis
    • 1
  • Dimitrios Letsios
    • 2
  • Giorgio Lucarelli
    • 1
    • 3
  1. 1.Sorbonne Universités, UPMC Univ. Paris 06, UMR 7606, LIP6ParisFrance
  2. 2.Institut für InformatikTechnische Universität MünchenMunichGermany
  3. 3.Université Grenoble-Alpes, INP, UMR 5217, LIGGrenobleFrance

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