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Sublinear time approximation schemes for makespan minimization on parallel machines

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Listed:
  • Bin Fu

    (University of Texas Rio Grande Valley)

  • Yumei Huo

    (CUNY)

  • Hairong Zhao

    (Purdue University Northwest)

Abstract

We study sublinear time algorithms for the classical makespan minimization problem of scheduling n jobs on m parallel machines. Under uniform random sampling setting, we consider the problem with constrained processing times, which remains NP-hard. We first consider the problem where the processing times of all jobs differ by no more than a constant factor c. We develop the first sublinear time approximation scheme for this problem when the number of machines m is at most $$\tfrac{n \epsilon }{20 c }$$ . We then extend our algorithm to the more general problem where the largest $$\alpha n$$ jobs have processing times that differ by no more than c factor for some constant $$\alpha $$ , $$0

Suggested Citation

  • Bin Fu & Yumei Huo & Hairong Zhao, 2025. "Sublinear time approximation schemes for makespan minimization on parallel machines," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 101(3), pages 507-528, June.
    • Handle: RePEc:spr:mathme:v:101:y:2025:i:3:d:10.1007_s00186-025-00898-z
    DOI: 10.1007/s00186-025-00898-z
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    References listed on IDEAS

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    1. D. Prot & O. Bellenguez-Morineau, 2018. "A survey on how the structure of precedence constraints may change the complexity class of scheduling problems," Journal of Scheduling, Springer, vol. 21(1), pages 3-16, February.
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