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Preemptive online scheduling with rejection of unit jobs on two uniformly related machines

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Abstract

We consider preemptive online and semi-online scheduling of unit jobs on two uniformly related machines. Jobs are presented one by one to an algorithm, and each job has a rejection penalty associated with it. A new job can either be rejected, in which case the algorithm pays its rejection penalty, or it can be scheduled preemptively on the machines, in which case it may increase the maximum completion time of any machine in the schedule, also known as the makespan of the constructed schedule. The objective is to minimize the sum of the makespan of the schedule of all accepted jobs and the total penalty of all rejected jobs. We study two versions of the problem. The first one is the online problem where the jobs arrive unsorted, and the second variant is the semi-online case, where the jobs arrive sorted by a non-increasing order of penalties. We also show that the variant where the jobs arrive sorted by a non-decreasing order of penalties is equivalent to the unsorted one. We design optimal online algorithms for both cases. These algorithms have smaller competitive ratios than the optimal competitive ratio for the more general problem with arbitrary processing times (except for the case of identical machines), but larger competitive ratios than the optimal competitive ratio for preemptive scheduling of unit jobs without rejection.

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References

  • Bartal, Y., Leonardi, S., Marchetti-Spaccamela, A., Sgall, J., & Stougie, L. (2000). Multiprocessor scheduling with rejection. SIAM Journal on Discrete Mathematics, 13(1), 64–78.

    Article  Google Scholar 

  • Bruno, J., & Gonzalez, T. (1976). Scheduling independent tasks with release dates and due dates on parallel machines. Technical report 213. University Park: Computer Science Department, The Pennsylvania State University.

  • Chen, B., van Vliet, A., & Woeginger, G. J. (1995). An optimal algorithm for preemptive on-line scheduling. Operations Research Letters, 18(3), 127–131.

    Article  Google Scholar 

  • Cho, Y., & Sahni, S. (1980). Bounds for list schedules on uniform processors. SIAM Journal on Computing, 9(1), 91–103.

    Article  Google Scholar 

  • Dósa, G., & He, Y. (2006). Preemptive and non-preemptive on-line algorithms for scheduling with rejection on two uniform machines. Computing, 76(1–2), 149–164.

    Article  Google Scholar 

  • Ebenlendr, T., Jawor, W., & Sgall, J. (2009). Preemptive online scheduling: Optimal algorithms for all speeds. Algorithmica, 53(4), 504–522.

    Article  Google Scholar 

  • Ebenlendr, T., & Sgall, J. (2011). Semi-online preemptive scheduling: One algorithm for all variants. Theory of Computing Systems, 48(3), 577–613.

    Article  Google Scholar 

  • Epstein, L. (2001). Optimal preemptive on-line scheduling on uniform processors with non-decreasing speed ratios. Operations Research Letters, 29(2), 93–98.

    Article  Google Scholar 

  • Epstein, L., & Favrholdt, L. M. (2002). Optimal preemptive semi-online scheduling to minimize makespan on two related machines. Operations Research Letters, 30(4), 269–275.

    Google Scholar 

  • Epstein, L., Noga, J., Seiden, S. S., Sgall, J., & Woeginger, G. J. (2001). Randomized online scheduling on two uniform machines. Journal of Scheduling, 4(2), 71–92.

    Article  Google Scholar 

  • Epstein, L., & Sgall, J. (2000). A lower bound for on-line scheduling on uniformly related machines. Operations Research Letters, 26(1), 17–22.

    Article  Google Scholar 

  • He, Y., & Min, X. (2000). On-line uniform machine scheduling with rejection. Computing, 65(1), 1–12.

    Google Scholar 

  • Horwath, E., Lam, E. C., & Sethi, R. (1977). A level algorithm for preemptive scheduling. Journal of the ACM, 24(1), 32–43.

    Article  Google Scholar 

  • Labetoulle, J., Lawler, E., Lenstra, J. K., Rinnooy Kan, A. H. G. (1984). Preemptive scheduling of uniform machines subject to release dates. In W. R. Pulleyblank (Ed.), Progress in combinatorial optimization (pp. 245–261). New York: Academic Press.

  • Seiden, S., Sgall, J., & Woeginger, G. (2000). Semi-online scheduling with decreasing job sizes. Operations Research Letters, 27(5), 215–221.

    Article  Google Scholar 

  • Seiden, S. S. (2001). Preemptive multiprocessor scheduling with rejection. Theoretical Computer Science, 262(1–2), 437–458.

    Article  Google Scholar 

  • Wen, J., & Du, D. (1998). Preemptive on-line scheduling for two uniform processors. Operations Research Letters, 23(3–5), 113–116.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Haifa, 3190501 , Haifa, Israel

    Leah Epstein & Hanan Zebedat-Haider

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  1. Leah Epstein
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  2. Hanan Zebedat-Haider
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Correspondence to Leah Epstein.

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Epstein, L., Zebedat-Haider, H. Preemptive online scheduling with rejection of unit jobs on two uniformly related machines. J Sched 17, 87–93 (2014). https://doi.org/10.1007/s10951-013-0326-0

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  • DOI: https://doi.org/10.1007/s10951-013-0326-0

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