A Truthful Constant Approximation for Maximizing the Minimum Load on Related Machines

  • George Christodoulou
  • Annamária Kovács
  • Rob van Stee
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6484)


Designing truthful mechanisms for scheduling on related machines is a very important problem in single-parameter mechanism design. We consider the covering objective, that is we are interested in maximizing the minimum completion time of a machine. This problem falls into the class of problems where the optimal allocation can be truthfully implemented. A major open issue for this class is whether truthfulness affects the polynomial-time implementation.

We provide the first constant factor approximation for deterministic truthful mechanisms. In particular we come up with a 2 + ε approximation guarantee, significantly improving on the previous upper bound of min(m,(2+ε)s m /s 1).


Polynomial Time Approximation Scheme Normal Segment Nondecreasing Order Related Machine Unrelated Machine 
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.


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  1. 1.
    Archer, A., Tardos, É.: Truthful mechanisms for one-parameter agents. In: Proc. 42nd Annual Symposium on Foundations of Computer Science, pp. 482–491 (2001)Google Scholar
  2. 2.
    Asadpour, A., Saberi, A.: An approximation algorithm for max-min fair allocation of indivisible goods. In: Proc. 39th Annual ACM Symp. Theory of Comp. (STOC), pp. 114–121. ACM, New York (2007)Google Scholar
  3. 3.
    Azar, Y., Epstein, L.: On-line machine covering. In: Burkard, R.E., Woeginger, G.J. (eds.) ESA 1997. LNCS, vol. 1284, pp. 23–36. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  4. 4.
    Azar, Y., Epstein, L.: Approximation schemes for covering and scheduling on related machines. In: Jansen, K., Rolim, J.D.P. (eds.) APPROX 1998. LNCS, vol. 1444, pp. 39–47. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  5. 5.
    Bateni, M., Charikar, M., Guruswami, V.: Maxmin allocation via degree lower-bounded arborescences. In: Proc. 41st Annual ACM Symp. Theory of Comp., pp. 543–552. ACM, New York (2009)Google Scholar
  6. 6.
    Chakrabarty, D., Chuzhoy, J., Khanna, S.: On allocating goods to maximize fairness. In: Proc. 50th Annual IEEE Symp. on Found. of Comp. Sci. (FOCS), pp. 107–116. IEEE Computer Society, Los Alamitos (2009)Google Scholar
  7. 7.
    Christodoulou, G., Kovács, A.: A deterministic truthful PTAS for scheduling related machines. In: Proc. 21st SIAM Symp. on Disc. Algs. (SODA), pp. 1005–1016. SIAM, Philadelphia (2010)Google Scholar
  8. 8.
    Dhangwatnotai, P., Dobzinski, S., Dughmi, S., Roughgarden, T.: Truthful approximation schemes for single-parameter agents. In: Proc. 49th IEEE Symp. on Found. of Comp. Sci., FOCS (2008)Google Scholar
  9. 9.
    Efraimidis, P.S., Spirakis, P.G.: Approximation schemes for scheduling and covering on unrelated machines. Theoretical Computer Science 359(1-3), 400–417 (2006)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Epstein, L., Sgall, J.: Approximation schemes for scheduling on uniformly related and identical parallel machines. Algorithmica 39(1), 43–57 (2004)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Epstein, L., van Stee, R.: Maximizing the minimum load for selfish agents. Theoretical Computer Science 411(1), 44–57 (2010)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Feige, U.: On allocations that maximize fairness. In: Proc. 19th annual ACM-SIAM Symp. Discr. Algs. (SODA), pp. 287–293. SIAM, Philadelphia (2008)Google Scholar
  13. 13.
    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)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Mu’alem, A., Schapira, M.: Setting lower bounds on truthfulness. In: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1143–1152 (2007)Google Scholar
  15. 15.
    Myerson, R.B.: Optimal auction design. Mathematics of Operations Research 6, 58–73 (1981)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Skutella, M., Verschae, J.: A robust PTAS for machine covering and packing. In: de Berg, M., Meyer, U. (eds.) ESA 2010. LNCS, vol. 6346, pp. 36–47. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  17. 17.
    Woeginger, G.J.: A polynomial time approximation scheme for maximizing the minimum machine completion time. Operations Research Letters 20(4), 149–154 (1997)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • George Christodoulou
    • 1
    • 3
  • Annamária Kovács
    • 2
  • Rob van Stee
    • 3
  1. 1.Cluster of Excellence “Multimodal Computing and Interaction”Saarland UniversitySaarbrückenGermany
  2. 2.Department of InformaticsGoethe UniversityFrankfurt am MainGermany
  3. 3.Max Planck Institute for InformaticsSaarbrückenGermany

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