Approximation Algorithms for Unrelated Machine Scheduling with an Energy Budget

  • Lin Chen
  • Wenchang Luo
  • Guochuan Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6681)


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.


Approximation algorithm Unrelated machine scheduling Rounding 


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  1. 1.
    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)Google Scholar
  2. 2.
    Alon, N., Azar, Y., Woeginger, G.J., Yadid, T.: Approximation schemes for scheduling on parallel machines. Journal of Scheduling 1, 55–66 (1998)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Grigoriev, A., Sviridenko, M., Uetz, M.: Machine scheduling with resource dependent processing times. Mathematical Programming 110(1), 209–228 (2007)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    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)CrossRefGoogle Scholar
  5. 5.
    Lenstra, J.K., Shmoys, D.B., Tardos, E.: Approximation algorithms for scheduling unrelated parallel machines. Mathematical Programming 46, 259–271 (1990)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    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)CrossRefGoogle Scholar
  7. 7.
    Pruhs, K., van Stee, R., Uthaisombut, P.: Speed scaling of tasks with precedence constraints. Theory of Computing Systems 43(1), 67–80 (2008)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Shchepin, E.V., Vakhania, N.: An optimal rounding gives a better approximation for scheduling unrelated machines. Operations Research Letters 33(2), 127–133 (2005)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    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)Google Scholar
  10. 10.
    Yao, F., Li, M.: An efficient algorithm for computing optimal discrete voltage schedules. SIAM Journal on Computing 35(3), 658–671 (2006)MathSciNetMATHGoogle Scholar
  11. 11.
    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)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Lin Chen
    • 1
  • Wenchang Luo
    • 2
  • Guochuan Zhang
    • 1
  1. 1.College of Computer ScienceZhejiang UniversityHangzhouChina
  2. 2.Faculty of ScienceNingbo UniversityNingboChina

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