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Scheduling Two Machines with Release Times

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Integer Programming and Combinatorial Optimization (IPCO 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1610))

Abstract

We present a deterministic online algorithm for scheduling two parallel machines when jobs arrive over time and show that it is \( (5 - \sqrt 5 )/2 \approx 1.38198\)-competitive. The best previously known algorithm is 3/2 -competitive. Our upper bound matches a previously known lower bound, and thus our algorithm has the best possible competitive ratio. We also present a lower bound of 1.21207 on the competitive ratio of any randomized online algorithm for any number of machines. This improves a previous result of \( 4 - 2\sqrt 2 ) \approx 1.17157\).

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References

  1. Albers, S. Better bounds for online scheduling. In Proceedings of the 29th ACM Symposium on Theory of Computing (1997), pp. 130–139.

    Google Scholar 

  2. Bartal, Y., Fiat, A., Karloff, H., and Vohra, R. New algorithms for an ancient scheduling problem. Journal of Computer and System Sciences 51,3 (Dec 1995), 359–366.

    Article  MathSciNet  Google Scholar 

  3. Bartal, Y., Karloff, H., and Rabani, Y. A better lower bound for on-line scheduling. Information Processing Letters 50,3 (May 1994), 113–116.

    Article  MATH  MathSciNet  Google Scholar 

  4. Chen, B., van Vliet, A., and Woeginger, G. A lower bound for randomized on-line scheduling algorithms. Information Processing Letters 51,5 (Sep 1994), 219–222.

    Article  MATH  MathSciNet  Google Scholar 

  5. Chen, B., van Vliet, A., and Woeginger, G. New lower and upper bounds for on-line scheduling. Operations Research Letters 16,4 (Nov 1994), 221–230.

    Article  MATH  MathSciNet  Google Scholar 

  6. CHEN, B., and VESTJENS, A. Scheduling on identical machines: How good is LPT in an online setting? Operations Research Letters 21,4 (Nov 1997), 165–169.

    Article  MATH  MathSciNet  Google Scholar 

  7. Faigle, U., Kern, W., and Turàan, G. On the performance of on-line algorithms for partition problems. Acta Cybernetica 9,2 (1989), 107–119.

    MATH  MathSciNet  Google Scholar 

  8. Galambos, G., and Woeginger, G. An online scheduling heuristic with better worst case ratio than Graham’s list scheduling. SIAM Journal on Computing 22,2 (Apr 1993), 349–355.

    Article  MATH  MathSciNet  Google Scholar 

  9. Graham, R. L. Bounds for certain multiprocessing anomalies. Bell Systems Technical Journal 45 (1966), 1563–1581.

    Google Scholar 

  10. Hall, L., and Shmoys, D. Approximation schemes for constrained scheduling problems. In Proceedings of the 30th IEEE Symposium on Foundations of Computer Science (1989), pp. 134–139.

    Google Scholar 

  11. Karger, D., Phillips, S., and Torng, E. A better algorithm for an ancient scheduling problem. Journal of Algorithms 20,2 (Mar 1996), 400–430.

    Article  MATH  MathSciNet  Google Scholar 

  12. Karlin, A., Manasse, M., Rudolph, L., and Sleator, D. Competitive snoopy caching. Algorithmica 3,1 (1988), 79–119.

    Article  MATH  MathSciNet  Google Scholar 

  13. Reingold, N., Westbrook, J., and Sleator, D. Randomized competitive algorithms for the list update problem. Algorithmica 11,1 (Jan 1994), 15–32.

    Article  MATH  MathSciNet  Google Scholar 

  14. Seiden, S. S. Randomized algorithms for that ancient scheduling problem. In Proceedings of the 5th Workshop on Algorithms and Data Structures (Aug 1997), pp. 210–223.

    Google Scholar 

  15. Sgall, J. A lower bound for randomized on-line multiprocessor scheduling. Information Processing Letters 63,1 (Jul 1997), 51–55.

    Article  MathSciNet  Google Scholar 

  16. Shmoys, D., Wein, J., and Williamson, D. Scheduling parallel machines online. In Proceedings of the 32nd Symposium on Foundations of Computer Science (Oct 1991), pp. 131–140.

    Google Scholar 

  17. Sleator, D., and Tarjan, R. Amortized efficiency of list update and paging rules. Communications of the ACM 28,2 (Feb 1985), 202–208.

    Article  MathSciNet  Google Scholar 

  18. Stougie, L., and Vestjens, A. P. A. Randomized on-line scheduling: How low can’t you go? Manuscript, 1997.

    Google Scholar 

  19. Vestjens, A. P. A.On-line Machine Scheduling. PhD thesis, Eindhoven University of Technology, The Netherlands, 1997.

    Google Scholar 

  20. Von Neumann, J., and Morgenstern, O.Theory of games and economic behavior, 1st ed. Princeton University Press, 1944.

    Google Scholar 

  21. Yao, A. C. Probabilistic computations: Toward a unified measure of complexity. In Proceedings of the 18th IEEE Symposium on Foundations of Computer Science (1977), pp. 222–227.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für Mathematik B, Technische Universität Graz, Steyrergasse 30/2. Stock, A-8010, Graz, Austria

    John Noga

  2. Max-Planck-Institute für Informatik Im Stadtwald, D-66123, Saarbrücken, Germany

    Steve Seiden

Authors
  1. John Noga
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  2. Steve Seiden
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Editor information

Editors and Affiliations

  1. GSIA, Carnegie Mellon University, Schenley Park, Pittsburgh, PA, 15213, USA

    Gérard Cornuéjols

  2. Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, A-8010, Graz, Austria

    Rainer E. Burkard  & Gerhard J. Woeginger  & 

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© 1999 Springer-Verlag Berlin Heidelberg

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Noga, J., Seiden, S. (1999). Scheduling Two Machines with Release Times. In: Cornuéjols, G., Burkard, R.E., Woeginger, G.J. (eds) Integer Programming and Combinatorial Optimization. IPCO 1999. Lecture Notes in Computer Science, vol 1610. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48777-8_29

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  • DOI: https://doi.org/10.1007/3-540-48777-8_29

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66019-4

  • Online ISBN: 978-3-540-48777-7

  • eBook Packages: Springer Book Archive

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