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Optimal On-Line Algorithms to Minimize Makespan on Two Machines with Resource Augmentation

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Abstract

We study the problem of on-line scheduling on two uniformly related machines where the on-line algorithm has resources different from those of the off-line algorithm. We consider three versions of this problem, preemptive semi-online, non-preemptive on-line and preemptive on-line scheduling. For all these cases we design algorithms with best possible competitive ratios as functions of the machine speeds.

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References

  1. Albers, S.: Better bounds for online scheduling. SIAM J. Comput. 29(2), 459–473 (1999)

    Article  MathSciNet  Google Scholar 

  2. Aspnes, J., Azar, Y., Fiat, A., Plotkin, S., Waarts, O.: On-line load balancing with applications to machine scheduling and virtual circuit routing. J. ACM 44, 486–504 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bansal, N., Dhamdhere, K., Könemann, J., Sinha, A.: Non-clairvoyant scheduling for minimizing mean slowdown. In: Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science (STACS’03), pp. 260–270 (2003)

  4. Bartal, Y., Karloff, H., Rabani, Y.: A better lower bound for on-line scheduling. Inf. Process. Lett. 50, 113–116 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bartal, Y., Fiat, A., Karloff, H., Vohra, R.: New algorithms for an ancient scheduling problem. J. Comput. Syst. Sci. 51(3), 359–366 (1995)

    Article  MathSciNet  Google Scholar 

  6. Berman, P., Coulston, C.: Speed is more powerful than clairvoyance. Nord. J. Comput. 6(2), 181–193 (1999)

    MATH  MathSciNet  Google Scholar 

  7. Berman, P., Charikar, M., Karpinski, M.: On-line load balancing for related machines. J. Algorithms 35(1), 108–121 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. Chen, B., van Vliet, A., Woeginger, G.J.: An optimal algorithm for preemptive on-line scheduling. Oper. Res. Lett. 18, 127–131 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  9. Dobson, G.: Scheduling independent tasks on uniform processors. SIAM J. Comput. 13(4), 705–716 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  10. Ebenlendr, T., Jawor, W., Sgall, J.: Preemptive online scheduling: optimal algorithms for all speeds. In: Proc. of the 14th Annual European Symposium on Algorithms (ESA2006), pp. 327–339 (2006)

  11. Epstein, L.: Optimal preemptive on-line scheduling on uniform processors with non-decreasing speed ratios. Oper. Res. Lett. 29(2), 93–98 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  12. Epstein, L., Favrholdt, L.M.: Optimal preemptive semi-online scheduling to minimize makespan on two related machines. Oper. Res. Lett. 30(4), 269–275 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  13. Epstein, L., Favrholdt, L.M.: Optimal non-preemptive semi-online scheduling on two related machines. J. Algorithms 57(1), 49–73 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  14. Epstein, L., Sgall, J.: A lower bound for on-line scheduling on uniformly related machines. Oper. Res. Lett. 26(1), 17–22 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  15. Epstein, L., Noga, J., Seiden, S.S., Sgall, J., Woeginger, G.J.: Randomized online scheduling on two uniform machines. J. Sched. 4(2), 71–92 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  16. Faigle, U., Kern, W., Turan, G.: On the performance of online algorithms for partition problems. Acta Cybernetica 9, 107–119 (1989)

    MATH  MathSciNet  Google Scholar 

  17. Fleischer, R., Wahl, M.: Online scheduling revisited. J. Sched. 3(5), 343–353 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  18. Friesen, D.K.: Tighter bounds for LPT scheduling on uniform processors. SIAM J. Comput. 16(3), 554–560 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  19. Gonzalez, T., Ibarra, O.H., Sahni, S.: Bounds for LPT schedules on uniform processors. SIAM J. Comput. 6(1), 155–166 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  20. Gormley, T., Reingold, N., Torng, E., Westbrook, J.: Generating adversaries for request-answer games. In: Proceedings of the Eleventh Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’2000), pp. 564–565 (2000)

  21. Graham, R.L.: Bounds for certain multiprocessing anomalies. Bell Syst. Tech. J. 45, 1563–1581 (1966)

    Google Scholar 

  22. Graham, R.L.: Bounds on multiprocessing timing anomalies. SIAM J. Appl. Math. 17, 416–429 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  23. Horwath, E., Lam, E.C., Sethi, R.: A level algorithm for preemptive scheduling. J. Assoc. Comput. Mach. 24, 32–43 (1977)

    MathSciNet  Google Scholar 

  24. Kalyanasundaram, B., Pruhs, K.: Speed is as powerful as clairvoyance. J. ACM 47(4), 214–221 (2000)

    Article  MathSciNet  Google Scholar 

  25. Kalyanasundaram, B., Pruhs, K.: Maximizing job completions online. J. Algorithms 49(1), 63–85 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  26. Karger, D., Phillips, S., Torng, E.: A better algorithm for an ancient scheduling problem. J. Algorithms 20(2), 400–430 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  27. Lam, T.W., To, K.K.: Trade-offs between speed and processor in hard-deadline scheduling. In: Proceedings of the Tenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’99), pp. 623–632 (1999)

  28. Mireault, P., Orlin, J.B., Vohra, R.V.: A parametric worst case analysis of the LPT heuristic for two uniform machines. Oper. Res. 45, 116–125 (1997)

    Article  MATH  Google Scholar 

  29. Rudin, J.F. III: Improved bounds for the on-line scheduling problem. Ph.D. thesis, The University of Texas at Dallas (May 2001)

  30. Seiden, S.: Preemptive multiprocessor scheduling with rejection. Theor. Comput. Sci. 262(1–2), 437–458 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  31. Seiden, S., Sgall, J., Woeginger, G.: Semi-online scheduling with decreasing job sizes. Oper. Res. Lett. 27(5), 215–221 (2000)

    Article  MathSciNet  Google Scholar 

  32. Sgall, J.: A lower bound for randomized on-line multiprocessor scheduling. Inf. Process. Lett. 63(1), 51–55 (1997)

    Article  MathSciNet  Google Scholar 

  33. Sleator, D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Commun. ACM 28, 202–208 (1985)

    Article  MathSciNet  Google Scholar 

  34. Wen, J., Du, D.: Preemptive on-line scheduling for two uniform processors. Oper. Res. Lett. 23, 113–116 (1998)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Haifa, 31905, Haifa, Israel

    Leah Epstein

  2. School of Computer Science, Tel-Aviv University, Ramat-Aviv, Tel-Aviv, Israel

    Arik Ganot

Authors
  1. Leah Epstein
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  2. Arik Ganot
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Correspondence to Leah Epstein.

Additional information

This work was submitted as a part of the M.Sc. thesis of the second author. A preliminary version of this paper appeared in the proceedings of The First Workshop on Approximation and Online Algorithms (WAOA’03), pages 109–122.

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Epstein, L., Ganot, A. Optimal On-Line Algorithms to Minimize Makespan on Two Machines with Resource Augmentation. Theory Comput Syst 42, 431–449 (2008). https://doi.org/10.1007/s00224-007-9007-8

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  • DOI: https://doi.org/10.1007/s00224-007-9007-8

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