A 3/2-Approximation Algorithm for Rate-Monotonic Multiprocessor Scheduling of Implicit-Deadline Tasks

  • Andreas Karrenbauer
  • Thomas Rothvoß
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6534)


We present a new approximation algorithm for rate-monotonic multiprocessor scheduling of periodic tasks with implicit deadlines. We prove that for an arbitrary parameter k ∈ ℕ it yields solutions with at most \((\frac{3}{2}+\frac{1}{k})OPT+9k\) many processors, thus it gives an asymptotic 3/2-approximation algorithm. This improves over the previously best known ratio of 7/4. Our algorithm can be implemented to run in time O(n 2), where n is the number of tasks. It is based on custom-tailored weights for the tasks such that a greedy maximal matching and subsequent partitioning by a first-fit strategy yields the result.


Schedule Problem Periodic Task Task Versus Multiprocessor Schedule Relative Deadline 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Liu, C.L., Layland, J.W.: Scheduling algorithms for multiprogramming in a hard-real-time environment. J. ACM 20(1), 46–61 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Buttazzo, G.: Hard Real-time Computing Systems: Predictable Scheduling Algorithms And Applications (Real-Time Systems Series) (2004)Google Scholar
  3. 3.
    Garey, M.R., Graham, R.L., Johnson, D.S., Yao, A.C.C.: Resource constrained scheduling as generalized bin packing. J. Combin. Theory Ser. A 21, 257–298 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Johnson, D.S.: Near-optimal bin packing algorithms. PhD thesis, MIT, Cambridge, MA (1973)Google Scholar
  5. 5.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Karmarkar, N., Karp, R.M.: An efficient approximation scheme for the one-dimensional bin-packing problem. In: FOCS 1982, pp. 312–320. IEEE, Los Alamitos (1982)Google Scholar
  7. 7.
    Coffman Jr., E.G., Garey, M.R., Johnson, D.S.: Approximation algorithms for bin-packing—an updated survey. In: Algorithm Design for Computer System Design. Springer, Heidelberg (1984)Google Scholar
  8. 8.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Liu, J.: Real-Time Systems. Prentice Hall PTR, Upper Saddle River (2000)Google Scholar
  10. 10.
    Bini, E., Buttazzo, G., Buttazzo, G.: A hyperbolic bound for the rate monotonic algorithm. In: ECRTS 2001, p. 59 (2001)Google Scholar
  11. 11.
    Eisenbrand, F., Rothvoß, T.: Static-priority Real-time Scheduling: Response Time Computation is NP-hard. In: RTSS (2008)Google Scholar
  12. 12.
    Audsley, A.N., Burns, A., Richardson, M., Tindell, K.: Applying new scheduling theory to static priority pre-emptive scheduling. Software Engineering Journal, 284–292 (1993)Google Scholar
  13. 13.
    Fisher, N., Baruah, S.: A fully polynomial-time approximation scheme for feasibility analysis in static-priority systems with arbitrary relative deadlines. In: ECRTS 2005, pp. 117–126 (2005)Google Scholar
  14. 14.
    Baruah, S.K., Pruhs, K.: Open problems in real-time scheduling. Journal of Scheduling (2009)Google Scholar
  15. 15.
    Leung, J.: Handbook of Scheduling: Algorithms, Models, and Performance Analysis. CRC Press, Inc., Boca Raton (2004)zbMATHGoogle Scholar
  16. 16.
    Dhall, S.K., Liu, C.L.: On a real-time scheduling problem. Operations Research 26(1), 127–140 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    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. Chapman & Hall/CRC, Boca Raton (2004)Google Scholar
  18. 18.
    Oh, Y., Son, S.H.: Allocating fixed-priority periodic tasks on multiprocessor systems. Real-Time Syst. 9(3), 207–239 (1995)CrossRefGoogle Scholar
  19. 19.
    Karrenbauer, A., Rothvoß, T.: An average-case analysis for rate-monotonic multiprocessor real-time scheduling. In: Fiat, A., Sanders, P. (eds.) ESA 2009. LNCS, vol. 5757, pp. 432–443. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  20. 20.
    Eisenbrand, F., Rothvoß, T.: A PTAS for static priority real-time scheduling with resource augmentation. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 246–257. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  21. 21.
    Baruah, S., Goossens, J.: Scheduling real-time tasks: Algorithms and complexity. In: Handbook of Scheduling — Algorithms, Models, and Performance Analysis (2004)Google Scholar
  22. 22.
    Gabow, H.N.: Data structures for weighted matching and nearest common ancestors with linking. In: SODA 1990 (1990)Google Scholar
  23. 23.
    Cook, W.J., Cunningham, W.H., Pulleyblank, W.R., Schrijver, A.: Combinatorial Optimization. John Wiley, New York (1997)CrossRefzbMATHGoogle Scholar
  24. 24.
    Schrijver, A.: Combinatorial Optimization: Polyhedra and Efficiency. Algorithms and Combinatorics, vol. 24. Springer, Heidelberg (2003)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Andreas Karrenbauer
    • 1
  • Thomas Rothvoß
    • 2
  1. 1.ZukunftskollegUniversity of KonstanzGermany
  2. 2.Institute of MathematicsÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland

Personalised recommendations