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Approximating weighted completion time via stronger negative correlation

Author

Listed:
  • Alok Baveja

    (Rutgers Business School)

  • Xiaoran Qu

    (Department of Electrical Engineering and Computer Science
    Montgomery Blair High School)

  • Aravind Srinivasan

    (University of Maryland)

Abstract

Minimizing the weighted completion time of jobs in the unrelated parallel machines model is a fundamental scheduling problem. The first $$(3/2 - c)$$ ( 3 / 2 - c ) –approximation algorithm for this problem, for some constant $$c > 0$$ c > 0 , was obtained in the work of Bansal et al. (SIAM J Comput, 2021). A key ingredient in this work was the first dependent-rounding algorithm with a certain guaranteed amount of negative correlation. We improve upon this guaranteed amount from 1/108 to 1/27, thus also improving upon the constant c in the algorithms of Bansal et al. and Li (SIAM J Comput, 2020) for weighted completion time. Given the now-ubiquitous role played by dependent rounding in scheduling and combinatorial optimization, our improved dependent rounding is also of independent interest.

Suggested Citation

  • Alok Baveja & Xiaoran Qu & Aravind Srinivasan, 2024. "Approximating weighted completion time via stronger negative correlation," Journal of Scheduling, Springer, vol. 27(4), pages 319-328, August.
    • Handle: RePEc:spr:jsched:v:27:y:2024:i:4:d:10.1007_s10951-023-00780-y
    DOI: 10.1007/s10951-023-00780-y
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