A PTAS for Static Priority Real-Time Scheduling with Resource Augmentation

  • Friedrich Eisenbrand
  • Thomas Rothvoß
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5125)

Abstract

We present a polynomial time approximation scheme for the real-time scheduling problem with fixed priorities when resource augmentation is allowed. For a fixed ε> 0, our algorithm computes an assignment using at most (1 + εOPT + 1 processors in polynomial time, which is feasible if the processors have speed 1 + ε. We also show that, unless P = NP, there does not exist an asymptotic FPTAS for this problem.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Baruah, S., Goossens, J.: Scheduling real-time tasks: Algorithms and complexity. In: Leung, J.Y.-T. (ed.) Handbook of Scheduling — Algorithms, Models, and Performance Analysis, ch. 28. Chapman & Hall/CRC, Boca Raton (2004)Google Scholar
  2. 2.
    Davari, S., Dhall, S.K.: On-line algorithms for allocating periodic-time-critical tasks on multiprocessor systems. Informatica (Slovenia) 19(1) (1995)Google Scholar
  3. 3.
    Dhall, S.K.: Approximation algorithms for scheduling time-critical jobs on multiprocessor systems. In: Leung, J.Y.-T. (ed.) Handbook of Scheduling — Algorithms, Models, and Performance Analysis, ch. 32, Chapman & Hall/CRC, Boca Raton (2004)Google Scholar
  4. 4.
    Fernandez de la Vega, W., Lueker, G.S.: Bin packing can be solved within 1 + ε in linear time. Combinatorica 1(4), 349–355 (1981)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Fisher, N., Baruah, S.: A fully polynomial-time approximation scheme for feasibility analysis in static-priority systems with arbitrary relative deadlines. In: ECRTS 2005: Proceedings of the 17th Euromicro Conference on Real-Time Systems (ECRTS 2005), pp. 117–126. IEEE Computer Society, Los Alamitos (2005)Google Scholar
  6. 6.
    Garey, M.R., Johnson, D.S.: Computers and Intractability. Freeman, San Francisco (1979)MATHGoogle Scholar
  7. 7.
    Johnson, D.S.: The NP-completeness column: an ongoing guide. J. Algorithms 13(3), 502–524 (1992)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Karmarkar, N., Karp, R.M.: An efficient approximation scheme for the one-dimensional bin-packing problem. In: 23rd annual symposium on foundations of computer science, Chicago, Ill., pp. 312–320. IEEE, New York (1982)CrossRefGoogle Scholar
  9. 9.
    Lenstra, H.W.: Integer programming with a fixed number of variables. Mathematics of Operations Research 8(4), 538–548 (1983)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Liebeherr, J., Burchard, A., Oh, Y., Son, S.H.: New strategies for assigning real-time tasks to multiprocessor systems. IEEE Trans. Comput. 44(12), 1429–1442 (1995)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Liu, C.L., Layland, J.W.: Scheduling algorithms for multiprogramming in a hard-real-time environment. J. ACM 20(1), 46–61 (1973)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Oh, Y., Son, S.H.: Allocating fixed-priority periodic tasks on multiprocessor systems. Real-Time Syst. 9(3), 207–239 (1995)CrossRefGoogle Scholar
  13. 13.
    Schuurman, P., Woeginger, G.: Approximation schemes – a tutorial. In: Möhring, R.H., Potts, C.N., Schulz, A.S., Woeginger, G.J., Wolsey, L.A. (eds.) Lectures on Scheduling (to appear, 2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Friedrich Eisenbrand
    • 1
  • Thomas Rothvoß
    • 1
  1. 1.Institute of MathematicsÉcole Polytechnique Féderale de LausanneLausanneSwitzerland

Personalised recommendations