Skip to main content
SpringerLink
Log in

Scheduling and Packing Malleable Tasks with Precedence Constraints of Bounded Width

  • Conference paper
Book cover Approximation and Online Algorithms (WAOA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5893))

Included in the following conference series:

Abstract

We study two related problems in non-preemptive scheduling and packing of malleable tasks with precedence constraints to minimize the makespan. We distinguish the scheduling variant, in which we allow the free choice of processors, and the packing variant, in which a task must be assigned to a contiguous subset of processors.

For precedence constraints of bounded width, we completely resolve the complexity status for any particular problem setting concerning width bound and number of processors, and give polynomial-time algorithms with best possible performance. For both, scheduling and packing malleable tasks, we present an FPTAS for the NP-hard problem variants and exact algorithms for all remaining special cases. To obtain the positive results, we do not require the common monotonous penalty assumption on processing times, whereas our hardness results hold even when assuming this restriction.

With the close relation between contiguous scheduling and strip packing, our FPTAS is the first (and best possible) constant factor approximation for (malleable) strip packing under special precedence constraints.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Augustine, J., Banerjee, S., Irani, S.: Strip packing with precedence constraints and strip packing with release times. In: Proceedings of SPAA, pp. 180–189 (2006)

    Google Scholar 

  2. Błażewicz, J., Liu, Z.: Scheduling multiprocessor tasks with chain constraints. European Journal of Operational Research 94(2), 231–241 (1996)

    Article  MATH  Google Scholar 

  3. Dilworth, R.P.: A decomposition theorem for partially ordered sets. Annals of Mathematics 51(1), 161–166 (1950)

    Article  MathSciNet  Google Scholar 

  4. Drozdowski, M.: Scheduling multiprocessor tasks: an overview. European Journal of Operational Research 94(2), 215–230 (1996)

    Article  MATH  Google Scholar 

  5. Duin, C.W., Sluis, E.V.: On the complexity of adjacent resource scheduling. Journal of Scheduling 9(1), 49–62 (2006)

    Article  MATH  Google Scholar 

  6. Fulkerson, D.R.: Note on Dilworth’s decomposition theorem for partially ordered sets. Proceedings of the American Mathematical Society 7(4), 701–702 (1956)

    Article  MATH  MathSciNet  Google Scholar 

  7. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, New York (1979)

    MATH  Google Scholar 

  8. Grigoriev, A., Woeginger, G.J.: Project scheduling with irregular costs: complexity, approximability, and algorithms. Acta Informatica 41(2–3), 83–97 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  9. Günther, E.: Bin Scheduling: Partitionieren verformbarer Jobs mit Nebenbedingungen. Master’s thesis, Technische Universität Berlin (2008) (in German)

    Google Scholar 

  10. Jansen, K., Thöle, R.: Approximation algorithms for scheduling parallel jobs: Breaking the approximation ratio of 2. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 234–245. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  11. Jansen, K., Zhang, H.: An approximation algorithm for scheduling malleable tasks under general precedence constraints. ACM Transactions on Algorithms 2(3), 416–434 (2006)

    Article  MathSciNet  Google Scholar 

  12. Lepère, R., Mounié, G., Trystram, D.: An approximation algorithm for scheduling trees of malleable tasks. European Journal of Operational Research 142(2), 242–249 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  13. Lepère, R., Trystram, D., Woeginger, G.J.: Approximation algorithms for scheduling malleable tasks under precedence constraints. International Journal of Foundations of Computer Science 13(4), 613–627 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  14. Leung, J.-T.: Handbook of Scheduling: Algorithms, Models, and Performance Analysis. Chapman and Hall/CRC (2004)

    Google Scholar 

  15. Möhring, R.H.: Computationally tractable classes of ordered sets. In: Rival, I. (ed.) Algorithms and Order, pp. 105–194. Kluwer Academic Publishers, Dordrecht (1989)

    Google Scholar 

  16. Steiner, G.: On the complexity of dynamic programming for sequencing problems with precedence constraints. Annals of Operations Research 26, 103–123 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  17. Turek, J., Wolf, J., Yu, P.: Approximate algorithms for scheduling parallelizable tasks. In: Proceedings of SPAA, pp. 323–332 (1992)

    Google Scholar 

  18. Verriet, J.: The complexity of scheduling graphs of bounded width subject to non-zero communication delays. Technical Report UU-CS-1997-01, Utrecht University (1997)

    Google Scholar 

  19. Woeginger, G.J.: When does a dynamic programming formulation guarantee the existence of a fully polynomial time approximation scheme (FPTAS)? INFORMS Journal on Computing 12(1), 57–74 (2000)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Mathematik, Technische Universität Berlin, Germany

    Elisabeth Günther & Felix G. König

  2. Max-Planck-Institut für Informatik, Saarbrücken, Germany

    Nicole Megow

Authors
  1. Elisabeth Günther
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Felix G. König
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nicole Megow
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. IBISC, CNRS FRE 3190, Université d’Evry Val d’Essonne, Place des Terasses, Tour Evry 2, 91000, Evry Cedex, France

    Evripidis Bampis

  2. Institute for Computer Science and Applied Mathematics, University of Kiel, Olshausenstr. 40, 24098, Kiel, Germany

    Klaus Jansen

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Günther, E., König, F.G., Megow, N. (2010). Scheduling and Packing Malleable Tasks with Precedence Constraints of Bounded Width. In: Bampis, E., Jansen, K. (eds) Approximation and Online Algorithms. WAOA 2009. Lecture Notes in Computer Science, vol 5893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12450-1_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-12450-1_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12449-5

  • Online ISBN: 978-3-642-12450-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation