Approximation Algorithm for Scheduling a Chain of Tasks on Heterogeneous Systems

  • Massinissa Ait Aba
  • Lilia Zaourar
  • Alix Munier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10659)


This paper presents an efficient approximation algorithm to solve the task scheduling problem on heterogeneous platform for the particular case of the linear chain of tasks. The objective is to minimize both the total execution time (makespan) and the total energy consumed by the system. For this purpose, we introduce a constraint on the energy consumption during execution. Our goal is to provides an algorithm with a performance guarantee. Two algorithms have been proposed; the first provides an optimal solution for preemptive scheduling. This solution is then used in the second algorithm to provide an approximate solution for non-preemptive scheduling. Numerical evaluations demonstrate that the proposed algorithm achieves a close-to-optimal performance compared to exact solution obtained by CPLEX for small instances. For large instances, CPLEX is struggling to provide a feasible solution, whereas our approach takes less than a second to produce a solution for an instance of 10000 tasks.


Linear chain of tasks Makespan Energy Approximation algorithm 


  1. 1.
    Aupy, G., Benoit, A., Dufossé, F., Robert, Y.: Reclaiming the energy of a schedule: models and algorithms. Concur. Comput.: Pract. Exp. 25(11), 1505–1523 (2013)CrossRefGoogle Scholar
  2. 2.
    Fard, H.M., Prodan, R., Barrionuevo, J.J.D., Fahringer, T.: A multi-objective approach for workflow scheduling in heterogeneous environments. In: Proceedings of the 2012 12th IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing (CCGRID 2012), pp. 300–309. IEEE Computer Society (2012)Google Scholar
  3. 3.
    Griessl, R., Peykanu, M., Hagemeyer, J., Porrmann, M., Krupop, S., Kosmann, L., Knocke, P., Kierzynka, M., Oleksiak, A., et al.: FPGA-accelerated heterogeneous hyperscale server architecture for next-generation compute clusters (2015)Google Scholar
  4. 4.
    IBM: IBM ILOG CPLEX V12.5 user’s manual for CPLEX (2013).
  5. 5.
    Lee, Y.C., Zomaya, A.Y.: Minimizing energy consumption for precedence-constrained applications using dynamic voltage scaling. In: 9th IEEE/ACM International Symposium on Cluster Computing and the Grid, CCGRID 2009, pp. 92–99. IEEE (2009)Google Scholar
  6. 6.
    Zaourar, L., Ait Aba, M., Briand, D., Philippe, J.M.: Modeling of applications and hardware to explore task mapping and scheduling strategies on a heterogeneous micro-server system (2017, to appear in IPDPSW)Google Scholar
  7. 7.
    Mezmaz, M., Melab, N., Kessaci, Y., Lee, Y.C., Talbi, E.G., Zomaya, A.Y., Tuyttens, D.: A parallel bi-objective hybrid metaheuristic for energy-aware scheduling for cloud computing systems. J. Parallel Distrib. Comput. 71(11), 1497–1508 (2011)CrossRefGoogle Scholar
  8. 8.
    Sheikh, H.F., Ahmad, I.: Efficient heuristics for joint optimization of performance, energy, and temperature in allocating tasks to multi-core processors. In: 2014 International Green Computing Conference (IGCC), pp. 1–8. IEEE (2014)Google Scholar
  9. 9.
    Tarplee, K.M., Friese, R., Maciejewski, A.A., Siegel, H.J.: Efficient and scalable pareto front generation for energy and makespan in heterogeneous computing systems. In: Fidanova, S. (ed.) Recent Advances in Computational Optimization. SCI, vol. 580, pp. 161–180. Springer, Cham (2015). Google Scholar
  10. 10.
    Tarplee, K.M., Friese, R., Maciejewski, A.A., Siegel, H.J., Chong, E.K.: Energy and makespan tradeoffs in heterogeneous computing systems using efficient linear programming techniques. IEEE Trans. Parallel Distrib. Syst. 27(6), 1633–1646 (2016)CrossRefGoogle Scholar
  11. 11.
    Vasquez Perez, O.C.: Ordonnancement de tâches pour concilier la minimisation de la consommation d’énergie avec la qualité de service: optimisation et théorie des jeux. Ph.D. thesis, Paris 6 (2014)Google Scholar
  12. 12.
    Xie, G., Xiao, X., Li, R., Li, K.: Schedule length minimization of parallel applications with energy consumption constraints using heuristics on heterogeneous distributed systems. Concurr. Comput.: Pract. Exp. (2016)Google Scholar
  13. 13.
    Young, B.D., Pasricha, S., Maciejewski, A.A., Siegel, H.J., Smith, J.T.: Heterogeneous makespan and energy-constrained DAG scheduling. In: Proceedings of the 2013 Workshop on Energy Efficient High Performance Parallel and Distributed Computing, pp. 3–12. ACM (2013)Google Scholar
  14. 14.
    Zhang, L., Li, K., Li, C., Li, K.: Bi-objective workflow scheduling of the energy consumption and reliability in heterogeneous computing systems. Inf. Sci. 379, 241–256 (2017)CrossRefGoogle Scholar
  15. 15.
    Zhang, L., Li, K., Xu, Y., Mei, J., Zhang, F., Li, K.: Maximizing reliability with energy conservation for parallel task scheduling in a heterogeneous cluster. Inf. Sci. 319, 113–131 (2015)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Zhong, X., Xu, C.Z.: Energy-aware modeling and scheduling for dynamic voltage scaling with statistical real-time guarantee. IEEE Trans. Comput. 56(3), 358–372 (2007)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Massinissa Ait Aba
    • 1
  • Lilia Zaourar
    • 1
  • Alix Munier
    • 2
  1. 1.CEA, LIST, Computing and Design Environment LaboratoryGif sur Yvette CedexFrance
  2. 2.LIP6-UPMCParisFrance

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