A Fast 5/2-Approximation Algorithm for Hierarchical Scheduling

  • Marin Bougeret
  • Pierre-François Dutot
  • Klaus Jansen
  • Christina Otte
  • Denis Trystram
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6271)

Abstract

We present in this article a new approximation algorithm for scheduling a set of n independent rigid (meaning requiring a fixed number of processors) jobs on hierarchical parallel computing platform. A hierarchical parallel platform is a collection of k parallel machines of different sizes (number of processors). The jobs are submitted to a central queue and each job must be allocated to one of the k parallel machines (and then scheduled on some processors of this machine), targeting the minimization of the maximum completion time (makespan). We assume that no job require more resources than available on the smallest machine.

This problem is hard and it has been previously shown that there is no polynomial approximation algorithm with a ratio lower than 2 unless P = NP. The proposed scheduling algorithm achieves a \({{5}\over{2}}\) ratio and runs in O(log(np max )knlog(n)), where p max is the maximum processing time of the jobs. Our results also apply for the Multi Strip Packing problem where the jobs (rectangles) must be allocated on contiguous processors.

Keywords

Parallel Machine Pack Procedure Maximum Completion Time Optimal Makespan Strip Packing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Foster, I., Kesselman, C., Tuecke, S.: The anatomy of the grid: Enabling scalable virtual organizations. International Journal of High Performance Computing Applications 15(3), 200 (2001)CrossRefGoogle Scholar
  2. 2.
    Feitelson, D.G., Rudolph, L., Schwiegelshohn, U., Sevcik, K.C., Wong, P.: Theory and practice in parallel job scheduling. In: JSSPP, pp. 1–34 (1997)Google Scholar
  3. 3.
    Zhuk, S.: Approximate algorithms to pack rectangles into several strips. Discrete Mathematics and Applications 16(1), 73–85 (2006)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Ye, D., Han, X., Zhang, G.: On-Line Multiple-Strip Packing. In: Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications (COCOA), p. 165. Springer, Heidelberg (2009)Google Scholar
  5. 5.
    Bougeret, M., Dutot, P.F., Jansen, K., Otte, C., Trystram, D.: Approximation algorithm for multiple strip packing. In: Bampis, E., Jansen, K. (eds.) WAOA 2010. LNCS, vol. 5893, pp. 37–48. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  6. 6.
    Pascual, F., Rzadca, K., Trystram, D.: Cooperation in multi-organization scheduling. In: Kermarrec, A.-M., Bougé, L., Priol, T. (eds.) Euro-Par 2007. LNCS, vol. 4641, pp. 224–233. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Schwiegelshohn, U., Tchernykh, A., Yahyapour, R.: Online scheduling in grids. In: IEEE International Symposium on Parallel and Distributed Processing, IPDPS 2008, pp. 1–10 (2008)Google Scholar
  8. 8.
    Steinberg, A.: A strip-packing algorithm with absolute performance bound 2. SIAM Journal on Computing 26, 401 (1997)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Hochbaum, D., Shmoys, D.: A polynomial approximation scheme for scheduling on uniform processors: Using the dual approximation approach. SIAM J. Comput. 17(3), 539–551 (1988)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Marin Bougeret
    • 1
  • Pierre-François Dutot
    • 1
  • Klaus Jansen
    • 2
  • Christina Otte
    • 2
  • Denis Trystram
    • 1
  1. 1.Grenoble UniversityMontbonnot Saint MartinFrance
  2. 2.Department of Computer ScienceChristian-Albrechts-University to KielKielGermany

Personalised recommendations