Controlling and Assessing Correlations of Cost Matrices in Heterogeneous Scheduling

  • Louis-Claude Canon
  • Pierre-Cyrille Héam
  • Laurent Philippe
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9833)


This paper considers the problem of allocating independent tasks to unrelated machines such as to minimize the maximum completion time. Testing heuristics for this problem requires the generation of cost matrices that specify the execution time of each task on each machine. Numerous studies showed that the task and machine heterogeneities belong to the properties impacting heuristics performance the most. This study focuses on orthogonal properties, the average correlations between each pair of rows and each pair of columns, which is a proximity measure with uniform instances (Uniform instances are particular unrelated instances in which each execution time is proportional to the weight of the task and the cycle time of the machine.). Cost matrices generated with a novel generation method show the effect of these correlations on the performance of several heuristics from the literature. In particular, EFT performance depends on whether the tasks are more correlated than the machines and HLPT performs the best when both correlations are close to one.



Computations have been performed on the supercomputer facilities of the Mésocentre de calcul de Franche-Comté.


  1. 1.
    Al-Qawasmeh, A.M., Maciejewski, A.A., Roberts, R.G., Siegel, H.J.: Characterizing task-machine affinity in heterogeneous computing environments. In: IPDPSW (2011)Google Scholar
  2. 2.
    Al-Qawasmeh, A.M., Maciejewski, A.A., Siegel, H.J.: Characterizing heterogeneous computing environments using singular value decomposition. In: IPDPSW (2010)Google Scholar
  3. 3.
    Al-Qawasmeh, A.M., Pasricha, S., Maciejewski, A.A., Siegel, H.J.: Power and thermal-aware workload allocation in heterogeneous data centers. Trans. Comput. 64(2), 477–491 (2013)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Ali, S., Siegel, H.J., Maheswaran, M., Hensgen, D.: Task execution time modeling for heterogeneous computing systems. In: HCW, pp. 185–199. IEEE (2000)Google Scholar
  5. 5.
    Ali, S., Siegel, H.J., Maheswaran, M., Hensgen, D., Ali, S.: Representing task and machine heterogeneities for heterogeneous computing systems. Tamkang J. Sci. Eng. 3(3), 195–208 (2000)Google Scholar
  6. 6.
    Canon, L.C., Héam, P.C., Philippe, L.: Controlling and Assessing Correlations of Cost Matrices in Heterogeneous Scheduling. Technical report RR-FEMTO-ST-1191, FEMTO-ST, February 2016Google Scholar
  7. 7.
    Canon, L.-C., Philippe, L.: On the heterogeneity bias of cost matrices when assessing scheduling algorithms. In: Träff, J.L., Hunold, S., Versaci, F. (eds.) Euro-Par 2015. LNCS, vol. 9233, pp. 109–121. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  8. 8.
    Canon, L.C., Philippe, L.: On the Heterogeneity Bias of Cost Matrices when Assessing Scheduling Algorithms. Technical report RR-FEMTO-ST-8663, FEMTO-ST, March 2015Google Scholar
  9. 9.
    Freund, R.F., Gherrity, M., Ambrosius, S., Campbell, M., Halderman, M., Hensgen, D., Keith, E., Kidd, T., Kussow, M., Lima, J.D., Mirabile, F., Moore, L., Rust, B., Siegel, H.J.: Scheduling resources in multi-user, heterogeneous, computing environments with SmartNet. In: HCW, pp. 184–199. IEEE (1998)Google Scholar
  10. 10.
    Graham, R.L.: Bounds on multiprocessing timing anomalies. J. appl. math. 17(2), 416–429 (1969)MathSciNetMATHGoogle Scholar
  11. 11.
    Ibarra, O.H., Kim, C.E.: Heuristic algorithms for scheduling independent tasks on nonidentical processors. J. ACM 24(2), 280–289 (1977)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Khemka, B., Friese, R., Pasricha, S., Maciejewski, A.A., Siegel, H.J., Koenig, G.A., Powers, S., Hilton, M., Rambharos, R., Poole, S.: Utility maximizing dynamic resource management in an oversubscribed energy-constrained heterogeneous computing system. Sustain. Comput. Inf. Syst. 5, 14–30 (2014)Google Scholar
  13. 13.
    Luo, P., Lü, K., Shi, Z.: A revisit of fast greedy heuristics for mapping a class of independent tasks onto heterogeneous computing systems. J. Parallel Distrib. Comput. 67(6), 695–714 (2007)CrossRefMATHGoogle Scholar
  14. 14.
    Maheswaran, M., Ali, S., Siegel, H.J., Hensgen, D., Freund, R.F.: Dynamic mapping of a class of independent tasks onto heterogeneous computing systems. J. Parallel Distrib. Comput. 59(2), 107–131 (1999)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Louis-Claude Canon
    • 1
  • Pierre-Cyrille Héam
    • 1
  • Laurent Philippe
    • 1
  1. 1.FEMTO-ST Institute/CNRS – Université de Franche-Comté/UBFCBesançonFrance

Personalised recommendations