Skip to main content
SpringerLink
Log in

Towards Tight Lower Bounds for Scheduling Problems

  • Conference paper
  • First Online:
Algorithms - ESA 2015

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9294))

Abstract

We show a close connection between structural hardness for k-partite graphs and tight inapproximability results for scheduling problems with precedence constraints. Assuming a natural but nontrivial generalisation of the bipartite structural hardness result of [1], we obtain a hardness of 2 − ε for the problem of minimising the makespan for scheduling precedence-constrained jobs with preemption on identical parallel machines. This matches the best approximation guarantee for this problem [6,4]. Assuming the same hypothesis, we also obtain a super constant inapproximability result for the problem of scheduling precedence-constrained jobs on related parallel machines, making progress towards settling an open question in both lists of ten open questions by Williamson and Shmoys [17], and by Schuurman and Woeginger [14].

The study of structural hardness of k-partite graphs is of independent interest, as it captures the intrinsic hardness for a large family of scheduling problems. Other than the ones already mentioned, this generalisation also implies tight inapproximability to the problem of minimising the weighted completion time for precedence-constrained jobs on a single machine, and the problem of minimising the makespan of precedence-constrained jobs on identical parallel machine, and hence unifying the results of Bansal and Khot[1] and Svensson [15], respectively.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Bansal, N., Khot, S.: Optimal long code test with one free bit. In: Proc. FOCS 2009, FOCS 2009, pp. 453–462. IEEE Computer Society, Washington, DC (2009)

    Google Scholar 

  2. Chekuri, C., Bender, M.: An efficient approximation algorithm for minimizing makespan on uniformly related machines. Journal of Algorithms 41(2), 212–224 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chudak, F.A., Shmoys, D.B.: Approximation algorithms for precedence-constrained scheduling problems on parallel machines that run at different speeds. Journal of Algorithms 30(2), 323–343 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  4. Gangal, D., Ranade, A.: Precedence constrained scheduling in (2-7/(3p+1)) optimal. Journal of Computer and System Sciences 74(7), 1139–1146 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. Gonzalez, T.F., Johnson, D.B.: A new algorithm for preemptive scheduling of trees. Journal of the ACM (JACM) 27(2), 287–312 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  6. Graham, R.L.: Bounds for certain multiprocessing anomalies. Bell System Technical Journal 45(9), 1563–1581 (1966)

    Article  MATH  Google Scholar 

  7. Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals of Discrete Mathematics 5(2), 287–326 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  8. Hochbaum, D.S., Shmoys, D.B.: Using dual approximation algorithms for scheduling problems theoretical and practical results. Journal of the ACM (JACM) 34(1), 144–162 (1987)

    Article  MathSciNet  Google Scholar 

  9. Hochbaum, D.S., Shmoys, D.B.: A polynomial approximation scheme for scheduling on uniform processors: Using the dual approximation approach. SIAM Journal on Computing 17(3), 539–551 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  10. Lenstra, J.K., Kan, A.R.: Computational complexity of discrete optimization problems. Annals of Discrete Mathematics 4, 121–140 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  11. McNaughton, R.: Scheduling with deadlines and loss functions. Management Science 6(1), 1–12 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  12. Muntz, R.R., Coffman Jr., E.G.: Optimal preemptive scheduling on two-processor systems. IEEE Transactions on Computers 100(11), 1014–1020 (1969)

    Article  MATH  Google Scholar 

  13. Muntz, R.R., Coffman Jr., E.G.: Preemptive scheduling of real-time tasks on multiprocessor systems. Journal of the ACM (JACM) 17(2), 324–338 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  14. Schuurman, P., Woeginger, G.J.: Polynomial time approximation algorithms for machine scheduling: Ten open problems. Journal of Scheduling 2(5), 203–213 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  15. Svensson, O.: Hardness of precedence constrained scheduling on identical machines. SIAM Journal on Computing 40(5), 1258–1274 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  16. Ullman, J.D.: Complexity of sequencing problems. In: Coman Jr., E.G. (ed.) Computer and Job-Shop Scheduling Theory (1976)

    Google Scholar 

  17. Williamson, D.P., Shmoys, D.B.: The design of approximation algorithms. Cambridge University Press (2011)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer and Communication Sciences, EPFL, Lausanne, Switzerland

    Abbas Bazzi & Ashkan Norouzi-Fard

Authors
  1. Abbas Bazzi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ashkan Norouzi-Fard
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abbas Bazzi .

Editor information

Editors and Affiliations

  1. University of Technology, Eindhoven, The Netherlands

    Nikhil Bansal

  2. Sapienza University of Rome, Rome, Italy

    Irene Finocchi

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bazzi, A., Norouzi-Fard, A. (2015). Towards Tight Lower Bounds for Scheduling Problems. In: Bansal, N., Finocchi, I. (eds) Algorithms - ESA 2015. Lecture Notes in Computer Science(), vol 9294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48350-3_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-48350-3_11

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-48349-7

  • Online ISBN: 978-3-662-48350-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation