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List’s worst-average-case or WAC ratio

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Abstract

We analyze the List scheduling algorithm for the problem of minimizing makespan using a worst-average-case or wac analysis technique, previously used by Kenyon for analyzing the Best Fit bin packing algorithm. We show that List’s worst-average-case or wac ratio asymptotically approaches 2, as m→∞. Thus, List’s worst-case behavior is not overly dependent on the order of job arrivals.

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References

  • Albers, S. (1999). Better bounds for online scheduling. SIAM Journal on Computing, 29, 459–473.

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Faigle, U., Kern, W., & Turán, G. (1989). On the performance of on-line algorithms for partition problems. Acta Informatica, 9, 107–119.

    Google Scholar 

  • Fleischer, R., & Wahl, M. (2000). On-line scheduling revisited. Journal of Scheduling, 3, 343–353.

    Article  Google Scholar 

  • Galambos, G., & Woeginger, G. (1993). An on-line scheduling heuristic with better worst case ratio than Graham’s list scheduling. SIAM Journal on Computing, 22, 349–355.

    Article  Google Scholar 

  • Gormley, T., Reingold, N., Torng, E., & Westbrook, J. (2000). Generating adversaries for request-answer games. In Symposium on discrete algorithms (SODA) (pp. 564–565)

  • Graham, R. L. (1966). Bounds for certain multiprocessor anomalies. Bell System Technical Journal, 45, 1563–1581.

    Google Scholar 

  • Karger, D., Phillips, S. J., & Torng, E. (1996). A better algorithm for an ancient scheduling problem. Journal of Algorithms, 20, 400–430.

    Article  Google Scholar 

  • Kenyon, C. (1996). Best-fit bin-packing with random order. In Symposium on discrete algorithms (SODA) (pp. 359–365).

  • Rudin III, J., & Chandrasekaran, R. (2003). Improved bounds for the online scheduling problem. SIAM Journal on Computing, 32, 717–735.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Christopher J. Osborn

  2. Department of Computer Science and Engineering, Michigan State University, East Lansing, MI, 48824, USA

    Eric Torng

Authors
  1. Christopher J. Osborn
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  2. Eric Torng
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Corresponding author

Correspondence to Eric Torng.

Additional information

C.J. Osborn is supported in part by NSF grant CCR 0105283. This work was done while the author was an undergraduate student at Michigan State University.

E. Torng is supported in part by NSF grant CCR 0105283.

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Osborn, C.J., Torng, E. List’s worst-average-case or WAC ratio. J Sched 11, 213–215 (2008). https://doi.org/10.1007/s10951-007-0019-7

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  • DOI: https://doi.org/10.1007/s10951-007-0019-7

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