Online Scheduling of Task Graphs on Hybrid Platforms

  • Louis-Claude Canon
  • Loris Marchal
  • Bertrand SimonEmail author
  • Frédéric Vivien
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11014)


Modern computing platforms commonly include accelerators. We target the problem of scheduling applications modeled as task graphs on hybrid platforms made of two types of resources, such as CPUs and GPUs. We consider that task graphs are uncovered dynamically, and that the scheduler has information only on the available tasks, i.e., tasks whose predecessors have all been completed. Each task can be processed by either a CPU or a GPU, and the corresponding processing times are known. Our study extends a previous \(4\sqrt{m/k}\)-competitive online algorithm [2], where m is the number of CPUs and k the number of GPUs (\(m\ge k\)). We prove that no online algorithm can have a competitive ratio smaller than \(\sqrt{m/k}\). We also study how adding flexibility on task processing, such as task migration or spoliation, or increasing the knowledge of the scheduler by providing it with information on the task graph, influences the lower bound. We provide a \((2\sqrt{m/k}+1)\)-competitive algorithm as well as a tunable combination of a system-oriented heuristic and a competitive algorithm; this combination performs well in practice and has a competitive ratio in \(\varTheta (\sqrt{m/k})\). Finally, simulations on different sets of task graphs illustrate how the instance properties impact the performance of the studied algorithms and show that our proposed tunable algorithm performs the best among the online algorithms in almost all cases and has even performance close to an offline algorithm.


Scheduling Heterogeneous computing Task graphs Online algorithms 


Data Availability Statement and Acknowledgments

The datasets generated during and/or analyzed during the current study are available in the Figshare repository:

This work was supported by the SOLHAR project (ANR-13-MONU-0007) which is operated by the French National Research Agency (ANR).


  1. 1.
    Agullo, E., Beaumont, O., Eyraud-Dubois, L., Kumar, S.: Are static schedules so bad? A case study on Cholesky factorization. In: IPDPS. IEEE (2016)Google Scholar
  2. 2.
    Amaris, M., Lucarelli, G., Mommessin, C., Trystram, D.: Generic algorithms for scheduling applications on hybrid multi-core machines. In: Rivera, F.F., Pena, T.F., Cabaleiro, J.C. (eds.) Euro-Par 2017. LNCS, vol. 10417, pp. 220–231. Springer, Cham (2017). Scholar
  3. 3.
    Augonnet, C., Clet-Ortega, J., Thibault, S., Namyst, R.: Data-aware task scheduling on multi-accelerator based platforms. In: ICPADS, pp. 291–298, December 2010Google Scholar
  4. 4.
    Augonnet, C., Thibault, S., Namyst, R., Wacrenier, P.A.: StarPU: a unified platform for task scheduling on heterogeneous multicore architectures. Concurr. Comput. Pract. Exp. 23(2), 187–198 (2011)CrossRefGoogle Scholar
  5. 5.
    Beaumont, O., Eyraud-Dubois, L., Kumar, S.: Approximation proofs of a fast and efficient list scheduling algorithm for task-based runtime systems on multicores and GPUs. In: IEEE IPDPS, pp. 768–777 (2017)Google Scholar
  6. 6.
    Beaumont, O., Cojean, T., Eyraud-Dubois, L., Guermouche, A., Kumar, S.: Scheduling of linear algebra kernels on multiple heterogeneous resources. In: HiPC (2016)Google Scholar
  7. 7.
    Bleuse, R., Gautier, T., Lima, J.V.F., Mounié, G., Trystram, D.: Scheduling data flow program in XKaapi: a new affinity based algorithm for heterogeneous architectures. In: Silva, F., Dutra, I., Santos Costa, V. (eds.) Euro-Par 2014. LNCS, vol. 8632, pp. 560–571. Springer, Cham (2014). Scholar
  8. 8.
    Bleuse, R., Kedad-Sidhoum, S., Monna, F., Mounié, G., Trystram, D.: Scheduling independent tasks on multi-cores with GPU accelerators. Concurr. Comput.: Pract. Exp. 27(6), 1625–1638 (2015)CrossRefGoogle Scholar
  9. 9.
    Canon, L.C., Marchal, L., Simon, B., Vivien, F.: Code for simulating online scheduling of task graphs on hybrid platforms, figshare, code (2018).
  10. 10.
    Canon, L.C., Marchal, L., Simon, B., Vivien, F.: Online scheduling of sequential task graphs on hybrid platforms. Research report 9150, INRIA, February 2018Google Scholar
  11. 11.
    Canon, L.-C., Marchal, L., Vivien, F.: Low-cost approximation algorithms for scheduling independent tasks on hybrid platforms. In: Rivera, F.F., Pena, T.F., Cabaleiro, J.C. (eds.) Euro-Par 2017. LNCS, vol. 10417, pp. 232–244. Springer, Cham (2017). Scholar
  12. 12.
    Chameleon, a dense linear algebra software for heterogeneous architectures.
  13. 13.
    Chen, L., Ye, D., Zhang, G.: Online scheduling of mixed CPU-GPU jobs. Int. J. Found. Comput. Sci. 25(06), 745–761 (2014)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Drozdowski, M.: Scheduling parallel tasks – algorithms and complexity. In: Leung, J. (ed.) Handbook of Scheduling. Chapman and Hall/CRC, Boca Raton (2004)Google Scholar
  15. 15.
    Feitelson, D.: Workload Modeling for Computer Systems Performance Evaluation, pp. 1–601. Cambridge University Press, Cambridge (2014). Book Draft, Version 1.0.1Google Scholar
  16. 16.
    Graham, R.L.: Bounds on multiprocessing timing anomalies. SIAM J. Appl. Math. 17(2), 416–429 (1969)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Imreh, C.: Scheduling problems on two sets of identical machines. Computing 70(4), 277–294 (2003)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Kedad-Sidhoum, S., Monna, F., Trystram, D.: Scheduling tasks with precedence constraints on hybrid multi-core machines. In: IEEE IPDPS Workshops, pp. 27–33 (2015)Google Scholar
  19. 19.
    Leung, J.Y.: Handbook of Scheduling: Algorithms, Models, and Performance Analysis. CRC Press, Boca Raton (2004)zbMATHGoogle Scholar
  20. 20.
    Beaumont, O., Eyraud-Dubois, L., Kumar, S.: Fast approximation algorithms for task-based runtime systems. Concurr. Comput.: Pract. Exper. Online version of record before inclusion in an issue
  21. 21.
    Raravi, G., Andersson, B., Nélis, V., Bletsas, K.: Task assignment algorithms for two-type heterogeneous multiprocessors. Real-Time Syst. 50(1), 87–141 (2014)CrossRefGoogle Scholar
  22. 22.
    Sainz, F., Mateo, S., Beltran, V., Bosque, J.L., Martorell, X., Ayguadé, E.: Leveraging OmpSs to exploit hardware accelerators. In: SBAC-PAD, pp. 112–119 (2014)Google Scholar
  23. 23.
    Tobita, T., Kasahara, H.: A standard task graph set for fair evaluation of multiprocessor scheduling algorithms. J. Sched. 5(5), 379–394 (2002)MathSciNetCrossRefGoogle Scholar
  24. 24.
    TOP500 Supercomputer Site. List of November 2017
  25. 25.
    Topcuoglu, H., Hariri, S., Wu, M.: Performance-effective and low-complexity task scheduling for heterogeneous computing. IEEE TPDS 13(3), 260–274 (2002)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Louis-Claude Canon
    • 1
    • 2
  • Loris Marchal
    • 2
  • Bertrand Simon
    • 2
    Email author
  • Frédéric Vivien
    • 2
  1. 1.FEMTO-ST Institute – Université de Bourgogne Franche-ComtéBesançonFrance
  2. 2.Univ Lyon, CNRS, ENS de Lyon, Inria, Université Claude-Bernard Lyon 1, LIP UMR5668Lyon Cedex 07France

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