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Multi-phase Algorithms for Throughput Maximization for Real-Time Scheduling

Author

Listed:
  • Piotr Berman

    (Pennsylvania State University)

  • Bhaskar Dasgupta

    (Rutgers University)

Abstract

We consider the problem of off-line throughput maximization for job scheduling on one or more machines, where each job has a release time, a deadline and a profit. Most of the versions of the problem discussed here were already treated by Bar-Noy et al. (Proc. 31st ACM STOC, 1999, pp. 622–631; http://www.eng.tau.ac.il/∼amotz/). Our main contribution is to provide algorithms that do not use linear programming, are simple and much faster than the corresponding ones proposed in Bar-Noy et al. (ibid., 1999), while either having the same quality of approximation or improving it. More precisely, compared to the results of in Bar-Noy et al. (ibid., 1999), our pseudo-polynomial algorithm for multiple unrelated machines and all of our strongly-polynomial algorithms have better performance ratios, all of our algorithms run much faster, are combinatorial in nature and avoid linear programming. Finally, we show that algorithms with better performance ratios than 2 are possible if the stretch factors of the jobs are bounded; a straightforward consequence of this result is an improvement of the ratio of an optimal solution of the integer programming formulation of the JISP2 problem (see Spieksma, Journal of Scheduling, vol. 2, pp. 215–227, 1999) to its linear programming relaxation.

Suggested Citation

  • Piotr Berman & Bhaskar Dasgupta, 2000. "Multi-phase Algorithms for Throughput Maximization for Real-Time Scheduling," Journal of Combinatorial Optimization, Springer, vol. 4(3), pages 307-323, September.
    • Handle: RePEc:spr:jcomop:v:4:y:2000:i:3:d:10.1023_a:1009822211065
    DOI: 10.1023/A:1009822211065
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    Citations

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    Cited by:

    1. de Weerdt, Mathijs & Baart, Robert & He, Lei, 2021. "Single-machine scheduling with release times, deadlines, setup times, and rejection," European Journal of Operational Research, Elsevier, vol. 291(2), pages 629-639.
    2. Zhi-Long Chen & Nicholas G. Hall, 2008. "Maximum Profit Scheduling," Manufacturing & Service Operations Management, INFORMS, vol. 10(1), pages 84-107, February.
    3. Elendner, Thomas, 2003. "Scheduling and combinatorial auctions: Lagrangean relaxation-based bonds for the WJISP," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 570, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    4. Jasper Jong & Marc Uetz, 2020. "The quality of equilibria for set packing and throughput scheduling games," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 321-344, March.
    5. Venkatesan T. Chakaravarthy & Anamitra R. Choudhury & Shalmoli Gupta & Sambudha Roy & Yogish Sabharwal, 2018. "Improved algorithms for resource allocation under varying capacity," Journal of Scheduling, Springer, vol. 21(3), pages 313-325, June.

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