Fast Monotone 3-Approximation Algorithm for Scheduling Related Machines

  • Annamária Kovács
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3669)


We consider the problem of scheduling n jobs to m machines of different speeds s.t. the makespan is minimized (Q||Cmax). We provide a fast and simple, deterministic monotone 3-approximation algorithm for Q||Cmax Monotonicity is relevant in the context of truthful mechanisms: when each machine speed is only known to the machine itself, we need to motivate that machines declare their true speeds to the scheduling mechanism. As shown by Archer and Tardos, such motivation is possible only if the scheduling algorithm used by the mechanism is monotone. The best previous monotone algorithm that is polynomial in m, was a 5-approximation by Andelman et al. A randomized 2-approximation method, satisfying a weaker definition of truthfulness, is given by Archer. As a core result, we prove the conjecture of Auletta et al., that the greedy algorithm (Lpt) is monotone if machine speeds are all integer powers of 2.


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  1. 1.
    Archer, A.: Mechanisms for Discrete Optimization with Rational Agents. PhD thesis, Cornell University (2004)Google Scholar
  2. 2.
    Archer, A., Tardos, É.: Truthful mechanisms for one-parameter agents. In: Proc. 42nd IEEE Symp. on Found. of Comp. Sci (FOCS), pp. 482–491 (2001)Google Scholar
  3. 3.
    Hochbaum, D.S., Shmoys, D.B.: A polynomial approximation scheme for scheduling on uniform processors: Using the dual approximation approach. SIAM J. Comp. 17(3), 539–551 (1988)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Horowitz, E., Sahni, S.: Exact and approximate algorithms for scheduling nonidentical processors. Journal of the ACM 23, 317–327 (1976)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Kovács, A.: Fast monotone 3-approximation algorithm for scheduling related machines, Extended version:
  6. 6.
    Johnson, D.S., Garey, M.R.: Computers and Intractability; A Guide to the Theory of NP-completeness. Freeman, San Francisco (1979)MATHGoogle Scholar
  7. 7.
    Azar, Y., Andelman, N., Sorani, M.: Truthful approximation mechanisms for scheduling selfish related machines. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 69–82. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Auletta, V., Ambrosio, P.: Deterministic monotone algorithms for scheduling on related machines. In: Persiano, G., Solis-Oba, R. (eds.) WAOA 2004. LNCS, vol. 3351, pp. 267–280. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  9. 9.
    Auletta, V., De Prisco, R., Penna, P., Persiano, G.: Deterministic truthful approximation mechanisms for scheduling related machines. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 608–619. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  10. 10.
    Ibarra, O.H., Gonzalez, T., Sahni, S.: Exact and approximate algorithms for scheduling nonidentical processors. Journal of the ACM 23, 317–327 (1976)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Annamária Kovács
    • 1
  1. 1.Max-Planck Institut für InformatikSaarbrückenGermany

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