The Lazy Bureaucrat Problem with Common Arrivals and Deadlines: Approximation and Mechanism Design

  • Laurent Gourvès
  • Jérôme Monnot
  • Aris T. Pagourtzis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8070)


We study the Lazy Bureaucrat scheduling problem (Arkin, Bender, Mitchell and Skiena [1]) in the case of common arrivals and deadlines. In this case the goal is to select a subset of given jobs in such a way that the total processing time is minimized and no other job can fit into the schedule. Our contribution comprises a linear time 4/3-approximation algorithm and an FPTAS, which respectively improve on a linear time 2-approximation algorithm and a PTAS given for the more general case of common deadlines [2,3]. We then consider a selfish perspective, in which jobs are submitted by players who may falsely report larger processing times, and show a tight upper bound of 2 on the approximation ratio of strategyproof mechanisms, even randomized ones. We conclude by introducing a maximization version of the problem and a dedicated greedy algorithm.


Stein Lution 


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  1. 1.
    Arkin, E.M., Bender, M.A., Mitchell, J.S.B., Skiena, S.: The lazy bureaucrat scheduling problem. Inf. Comput. 184, 129–146 (2003)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Esfahbod, B., Ghodsi, M., Sharifi, A.: Common-deadline lazy bureaucrat scheduling problems. In: Dehne, F., Sack, J.-R., Smid, M. (eds.) WADS 2003. LNCS, vol. 2748, pp. 59–66. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  3. 3.
    Gai, L., Zhang, G.: On lazy bureaucrat scheduling with common deadlines. J. Comb. Optim. 15, 191–199 (2008)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Hepner, C., Stein, C.: Minimizing makespan for the lazy bureaucrat problem. In: Penttonen, M., Schmidt, E.M. (eds.) SWAT 2002. LNCS, vol. 2368, pp. 40–50. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  5. 5.
    Lin, M., Yang, Y., Xu, J.: On lazy bin covering and packing problems. In: Chen, D.Z., Lee, D.T. (eds.) COCOON 2006. LNCS, vol. 4112, pp. 340–349. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Lin, M., Yang, Y., Xu, J.: Improved approximation algorithms for maximum resource bin packing and lazy bin covering problems. In: Asano, T. (ed.) ISAAC 2006. LNCS, vol. 4288, pp. 567–577. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Epstein, L., Levin, A.: Asymptotic fully polynomial approximation schemes for variants of open-end bin packing. Inf. Process. Lett. 109, 32–37 (2008)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Gai, L., Zhang, G.: Hardness of lazy packing and covering. Oper. Res. Lett. 37, 89–92 (2009)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms. The MIT Press (2009)Google Scholar
  10. 10.
    Christodoulou, G., Gourvès, L., Pascual, F.: Scheduling selfish tasks: About the performance of truthful algorithms. In: Lin, G. (ed.) COCOON 2007. LNCS, vol. 4598, pp. 187–197. Springer, Heidelberg (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Laurent Gourvès
    • 1
    • 2
  • Jérôme Monnot
    • 1
    • 2
  • Aris T. Pagourtzis
    • 3
  1. 1.CNRS UMR 7243France
  2. 2.PSL Université Paris DauphineParis Cedex 16France
  3. 3.School of Electrical and Computer EngineeringNational Technical University of Athens (NTUA)ZographouGreece

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