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The On-Line Multiprocessor Scheduling Problem with Known Sum of the Tasks

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Abstract

In this paper we investigate a semi on-line multiprocessor scheduling problem. The problem is the classical on-line multiprocessor problem where the total sum of the tasks is known in advance. We show an asymptotic lower bound on the performance ratio of any algorithm (as the number of processors gets large), and present an algorithm which has performance ratio at most \(\tfrac{{\sqrt 6 + 1}}{2} < 1.725\) for any number of processors. When compared with known general lower bounds, this result indicates that the information on the sum of tasks substantially improves the performance ratio of on-line algorithms.

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REFERENCES

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

    Google Scholar 

  2. Angelelli, E., ”Semi on-line scheduling on two parallel processors with known sum and lower bound on the size of the tasks, ”Central Europ. J. of Oper. Res., 8, 285–295 (2000).

    Google Scholar 

  3. Angelelli, E., M. G. Speranza, and Zs. Tuza, ”Semi on-line scheduling on two parallel processors with upper bound on the items, ”Algorithmica, 37, 243–262 (2003).

    Google Scholar 

  4. Angelelli, E., M. G. Speranza, and Zs. Tuza, ”Semi on-line scheduling on three processors with known sum of the tasks, ”submitted.

  5. Azar, Y. and O. Regev, ”On-line bin-stretching, ”Theoretical Computer Science, 268, 17–41 (2001).

    Google Scholar 

  6. Faigle, U., W. Kern, and Gy. Tur ´an, ”On the performance of on-line algorithms for particular problems, ”Acta Cybernetica, 9, 107–119 (1989).

    Google Scholar 

  7. Fleischer, R. and M. Wahl, ”On-Line scheduling revisited, ”Journal of Scheduling, 3, 343–353 (2000).

    Google Scholar 

  8. Girlich, E., V. Kotov, and M. Kovalev, ”Semi on-line algorithm for multiprocessor scheduling problem with a given total processing time, ”Technical Report 98-05, The Mathematical Department, University Magdeburg, Germany, 1998.

    Google Scholar 

  9. He, Y. and G. Zhang, ”Semi on-line scheduling on two identical machines, ”Computing, 62, 179–187(1999).

    Google Scholar 

  10. Kellerer, H., V. Kotov, M. G. Speranza, and Zs. Tuza, ”Semi on-line algorithms for the partition problem, ”Oper. Res. Letters, 21, 235–242 (1997).

    Google Scholar 

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Authors and Affiliations

  1. Department of Quantitative Methods, University of Brescia, C.da S. Chiara 50, I-25122, Brescia, Italy

    E. Angelelli & M.G. Speranza

  2. Department of Computer Science, University of Veszprém, Hungary. Research supported in part by the Hungarian Scientific Research Fund, grant OTKA T029309

    Á.B. Nagy

  3. Comp. and Autom. Inst., Hungarian Academy of Sciences, Budapest, Hungary and Department of Computer Science, University of Veszprém, Hungary. Research supported in part by the Hungarian Scientific Research Fund, grant OTKA T032969

    Zs. Tuza

Authors
  1. E. Angelelli
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  2. Á.B. Nagy
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  3. M.G. Speranza
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  4. Zs. Tuza
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Correspondence to E. Angelelli.

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Angelelli, E., Nagy, Á., Speranza, M. et al. The On-Line Multiprocessor Scheduling Problem with Known Sum of the Tasks. Journal of Scheduling 7, 421–428 (2004). https://doi.org/10.1023/B:JOSH.0000046074.03560.5d

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  • DOI: https://doi.org/10.1023/B:JOSH.0000046074.03560.5d

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