A Unified Framework for Designing EPTAS’s for Load Balancing on Parallel Machines

  • Ishai Kones
  • Asaf LevinEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10936)


We consider a general load balancing problem on parallel machines. Our machine environment in particular generalizes the standard models of identical machines, and the model of uniformly related machines, as well as machines with a constant number of types, and machines with activation costs. The objective functions that we consider contain in particular the makespan objective and the minimization of the \(\ell _p\)-norm of the vector of loads of the machines, and each case allow the possibility of job rejection.

We consider this general model and design an efficient polynomial time approximation scheme (EPTAS) that applies for all its previously-studied special cases. This EPTAS improves the current best approximation scheme for some of these cases where only a polynomial time approximation scheme (PTAS) was known into an EPTAS.


Efficient Polynomial Time Approximation Scheme (EPTAS) Makespan Total Rejection Penalty Mixed Integer Linear Program (MILP) Dual Approximation Method 
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.


  1. 1.
    Alon, N., Azar, Y., Woeginger, G.J., Yadid, T.: Approximation schemes for scheduling on parallel machines. J. Sched. 1(1), 55–66 (1998)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bartal, Y., Leonardi, S., Marchetti-Spaccamela, A., Sgall, J., Stougie, L.: Multiprocessor scheduling with rejection. SIAM J. Discrete Math. 13(1), 64–78 (2000)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bonifaci, V., Wiese, A.: Scheduling unrelated machines of few different types. (2012)
  4. 4.
    Cesati, M., Trevisan, L.: On the efficiency of polynomial time approximation schemes. Inf. Process. Lett. 64(4), 165–171 (1997)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer-Verlag, Berlin (1999). Scholar
  6. 6.
    Epstein, L., Levin, A.: An efficient polynomial time approximation scheme for load balancing on uniformly related machines. Math. Progr. 147, 1–23 (2013)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Epstein, L., Levin, A.: Minimum total weighted completion time: Faster approximation schemes. (2014)
  8. 8.
    Epstein, L., Sgall, J.: Approximation schemes for scheduling on uniformly related and identical parallel machines. Algorithmica 39(1), 43–57 (2004)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer-Verlag, Berlin (2006). Scholar
  10. 10.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1979)zbMATHGoogle Scholar
  11. 11.
    Gehrke, J.C., Jansen, K., Kraft, S.E.J., Schikowski, J.: A PTAS for scheduling unrelated machines of few different types. In: Freivalds, R.M., Engels, G., Catania, B. (eds.) SOFSEM 2016. LNCS, vol. 9587, pp. 290–301. Springer, Heidelberg (2016). Scholar
  12. 12.
    Hochbaum, D.S.: Various notions of approximations: good, better, best and more. In: Hochbaum, D.S. (ed.) Approximation Algorithms. PWS Publishing Company (1997)Google Scholar
  13. 13.
    Hochbaum, D.S., Shmoys, D.B.: Using dual approximation algorithms for scheduling problems: theoretical and practical results. J. ACM 34(1), 144–162 (1987)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Hochbaum, D.S., Shmoys, D.B.: A polynomial approximation scheme for scheduling on uniform processors: using the dual approximation approach. SIAM J. Comput. 17(3), 539–551 (1988)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Jansen, K.: An EPTAS for scheduling jobs on uniform processors: using an MILP relaxation with a constant number of integral variables. SIAM J. Discrete Math. 24(2), 457–485 (2010)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Jansen, K., Maack, M.: An EPTAS for scheduling on unrelated machines of few different types. Algorithms and Data Structures. LNCS, vol. 10389, pp. 497–508. Springer, Cham (2017). Scholar
  17. 17.
    Jansen, K., Maack, M.: An EPTAS for scheduling on unrelated machines of few different types. CoRR, abs/1701.03263 (v2) (2017)Google Scholar
  18. 18.
    Kannan, R.: Improved algorithms for integer programming and related lattice problems. In: Proceedings of STOC 1983, pp. 193–206 (1983)Google Scholar
  19. 19.
    Khuller, S., Li, J., Saha, B.: Energy efficient scheduling via partial shutdown. In: Proceedings of SODA 2010, pp. 1360–1372 (2010)CrossRefGoogle Scholar
  20. 20.
    Lenstra Jr., H.W.: Integer programming with a fixed number of variables. Math. Oper. Res. 8(4), 538–548 (1983)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Marx, D.: Parameterized complexity and approximation algorithms. Comput. J. 51(1), 60–78 (2008)CrossRefGoogle Scholar
  22. 22.
    Schuurman, P., Woeginger, G.J.: Approximation schemes - a tutorial (2001).
  23. 23.
    Wiese, A., Bonifaci, V., Baruah, S.K.: Partitioned EDF scheduling on a few types of unrelated multiprocessors. Real-Time Syst. 49(2), 219–238 (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Industrial Engineering and ManagementThe TechnionHaifaIsrael

Personalised recommendations