Skip to main content
SpringerLink
Log in

A Fixed-Parameter Algorithm for Scheduling Unit Dependent Tasks with Unit Communication Delays

  • Conference paper
  • First Online:
Euro-Par 2021: Parallel Processing (Euro-Par 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12820))

Included in the following conference series:

Abstract

This paper considers the minimization of the makespan for a set of dependent tasks with unit duration and unit communication delays. Given an upper bound of the makespan, release dates and deadlines of the tasks can be computed. Time windows are defined accordingly. We prove that our scheduling problem is fixed-parameter tractable; the parameter is the maximum number of tasks that are schedulable at the same time considering time windows.

A fixed-parameter algorithm based on a dynamic programming approach is developed and proved to solve this optimization problem. This is, as far as we know, the first fixed-parameter algorithm for a scheduling problem with communication delays.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Ait Aba, M., Munier Kordon, A., Pallez (Aupy), G.: Scheduling on two unbounded resources with communication costs. In: Yahyapour, R. (ed.) Euro-Par 2019. LNCS, vol. 11725, pp. 117–128. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-29400-7_9

    Chapter  Google Scholar 

  2. Ait El Cadi, A., Ben Atitallah, R., Hanafi, S., Mladenović, N., Artiba, A.: New MIP model for multiprocessor scheduling problem with communication delays. Optimization Letters 11(6), 1091–1107 (2014). https://doi.org/10.1007/s11590-014-0802-2

    Article  MathSciNet  MATH  Google Scholar 

  3. Andronikos, T., Koziris, N., Papakonstantinou, G., Tsanakas, P.: Optimal scheduling for UET/UET-UCT generalized n-dimensional grid task graphs. J. Parallel Distrib. Comput. 57(2), 140–165 (1999)

    Article  Google Scholar 

  4. Bodlaender, H.L.: A tourist guide through treewidth. Acta Cybern. 11, 1–21 (1992)

    MathSciNet  MATH  Google Scholar 

  5. Chrétienne, P.: A polynomial algorithm to optimally schedule tasks on a virtual distributed system under tree-like precedence constraints. Eur. J. Oper. Res. 43(2), 225–230 (1989)

    Article  MathSciNet  Google Scholar 

  6. Chrétienne, P., Picouleau, C.: Scheduling with communication delays: a survey, pp. 65–90 (1995)

    Google Scholar 

  7. Cygan, M., et al.: Parameterized Algorithms. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21275-3

    Book  MATH  Google Scholar 

  8. Davidović, T., Liberti, L., Maculan, N., Mladenovic, N.: Towards the optimal solution of the multiprocessor scheduling problem with communication delays. In: MISTA Conference (2007)

    Google Scholar 

  9. Downey, R.G., Fellows, M.R.: Fundamentals of Parameterized Complexity. TCS. Springer, London (2013). https://doi.org/10.1007/978-1-4471-5559-1

    Book  MATH  Google Scholar 

  10. Drozdowski, M.: Scheduling for Parallel Processing. Springer, Heidelberg (2009). https://doi.org/10.1007/978-1-84882-310-5

  11. Giroudeau, R., Koenig, J.C.: Scheduling with communication delays. In: Levner, E. (ed.) Multiprocessor Scheduling, chap. 4. IntechOpen, Rijeka (2007)

    Google Scholar 

  12. Graham, R.L., Lawler, E., Lenstra, J., Rinnooy Kan, A.: Optimization and approximation in deterministic sequencing and scheduling: a survey. In: Hammer, P., Johnson, E., Korte, B. (eds.) Discrete Optimization II, Annals of Discrete Mathematics, vol. 5, pp. 287–326. Elsevier (1979)

    Google Scholar 

  13. Hoogeveen, J., Lenstra, J., Veltman, B.: Three, four, five, six, or the complexity of scheduling with communication delays. Oper. Res. Lett. 16(3), 129–137 (1994)

    Article  MathSciNet  Google Scholar 

  14. Mnich, M., Van Bevern, R.: Parameterized complexity of machine scheduling: 15 open problems. Comput. Oper. Res. 100, 254–261 (2018)

    Google Scholar 

  15. Munier Kordon, A.: A fixed-parameter algorithm for scheduling unit dependent tasks on parallel machines with time windows. Discrete Appl. Math. 290, 1–6 (2021)

    Article  MathSciNet  Google Scholar 

  16. Möhring, R.H., Schäffter, M.W.: Scheduling series-parallel orders subject to 0/1-communication delays. Parallel Comput. 25(1), 23–40 (1999)

    Article  MathSciNet  Google Scholar 

  17. Orr, M., Sinnen, O.: Optimal task scheduling benefits from a duplicate-free state-space. J. Parallel Distrib. Comput. 146, 158–174 (2020)

    Google Scholar 

  18. Rayward-Smith, V.: UET scheduling with unit interprocessor communication delays. Discrete Appl. Math. 18(1), 55–71 (1987)

    Article  MathSciNet  Google Scholar 

  19. Shimada, K., Taniguchi, I., Tomiyama, H.: Communication-aware scheduling for malleable tasks. In: 2019 International Conference on Platform Technology and Service (PlatCon), pp. 1–6 (2019)

    Google Scholar 

  20. Sinnen, O.: Reducing the solution space of optimal task scheduling. Comput. Oper. Res. 43, 201–214 (2014)

    Article  MathSciNet  Google Scholar 

  21. Veltman, B., Lageweg, B., Lenstra, J.: Multiprocessor scheduling with communication delays. Parallel Comput. 16(2), 173–182 (1990)

    Article  Google Scholar 

  22. Veltman, B.: Multiprocessor scheduling with communication delays. Ph.D. thesis, Eindhoven University of Technology (1993)

    Google Scholar 

  23. Venugopalan, S., Sinnen, O.: ILP formulations for optimal task scheduling with communication delays on parallel systems. IEEE Trans. Parallel Distrib. Syst. 26(1), 142–151 (2015)

    Article  Google Scholar 

  24. Zinder, Y., Su, B., Singh, G., Sorli, R.: Scheduling UET-UCT tasks: branch-and-bound search in the priority space. Optim. Eng. 11, 627–646 (2010)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sorbonne Université, CNRS, LIP6, 75005, Paris, France

    Ning Tang & Alix Munier Kordon

Authors
  1. Ning Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alix Munier Kordon
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ning Tang .

Editor information

Editors and Affiliations

  1. Universidade de Lisboa, Lisbon, Portugal

    Leonel Sousa

  2. Universidade de Lisboa, Lisbon, Portugal

    Nuno Roma

  3. Universidade de Lisboa, Lisbon, Portugal

    Pedro Tomás

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Tang, N., Kordon, A.M. (2021). A Fixed-Parameter Algorithm for Scheduling Unit Dependent Tasks with Unit Communication Delays. In: Sousa, L., Roma, N., Tomás, P. (eds) Euro-Par 2021: Parallel Processing. Euro-Par 2021. Lecture Notes in Computer Science(), vol 12820. Springer, Cham. https://doi.org/10.1007/978-3-030-85665-6_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-85665-6_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-85664-9

  • Online ISBN: 978-3-030-85665-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation