Simultaneous Approximation Ratios for Parallel Machine Scheduling Problems

  • Long Wan
  • Jin-Jiang YuanEmail author


Motivated by the problem to approximate all feasible schedules by one schedule in a given scheduling environment, we introduce in this paper the concepts of strong simultaneous approximation ratio and weak simultaneous approximation ratio. Then we study the two variants under various scheduling environments, such as non-preemptive, preemptive or fractional scheduling on identical, related or unrelated machines.


Scheduling Simultaneous approximation ratio Global fairness 

Mathematics Subject Classification

90B35 90C27 



The authors would like to thank the associate editor and two anonymous referees for their constructive comments and helpful suggestions.


  1. 1.
    Csirik, J., Kellerer, H., Woeginger, G.: The exact LPT-bound of maximizing the minimum completion time. Oper. Res. Lett. 11, 281–287 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Deuermeyer, B.L., Friesen, D.K., Langston, A.M.: Scheduling to maximize the minimum processor finish time in a multiprocessor system. SIAM J. Discrete Math. 3, 190–196 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Graham, R.L.: Bounds for certain multiprocessing anomalies. Bell Syst. Tech. J. 45, 1563–1581 (1966)CrossRefzbMATHGoogle Scholar
  4. 4.
    Graham, R.L.: Bounds for multiprocessing timing anomalies. SIAM J. Appl. Math. 17, 416–429 (1969)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    McNaughton, R.: Scheduling with deadlines and loss functions. Manag. Sci. 6, 1–12 (1959)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Bhargava, R., Goel, A., Meyerson, A.: Using approximate majorization to characterize protocol fairness. In: Proceedings of the 2001 ACM Special Interest Group for the computer systems performance evaluation community. International Conference on Measurement and Modeling of Computer Systems, pp. 330–331. ACM, New York (2001)Google Scholar
  7. 7.
    Goel, A., Meyerson, A., Plotkin, S.: Combining fairness with throughput: online routing with multiple objectives. J. Comput. Syst. Sci. 63, 62–79 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Goel, A., Meyerson, A., Plotkin, S.: Approximate majorization and fair online load balancing. ACM Trans. Algorithms 1, 338–349 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Kleinberg, J., Rabani, Y., Tardos, É.: Fairness in routing and load balancing. J. Comput. Syst. Sci. 63, 2–20 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Kumar, A., Kleinberg, J.: Fairness measures for resource allocation. SIAM J. Comput. 36, 657–680 (2006)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Information TechnologyJiangxi University of Finance and EconomicsNanchangChina
  2. 2.School of Mathematics and StatisticsZhengzhou UniversityZhengzhouChina

Personalised recommendations