Sublinear time approximation schemes for makespan minimization on parallel machines

Bin Fu (), Yumei Huo () and Hairong Zhao ()
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Bin Fu: University of Texas Rio Grande Valley
Yumei Huo: CUNY
Hairong Zhao: Purdue University Northwest

Mathematical Methods of Operations Research, 2025, vol. 101, issue 3, No 5, 507-528

Abstract: 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

Keywords: Makespan minimization; Parallel machine; Sublinear time algorithms; Uniform sampling; Precedence constraints (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00186-025-00898-z

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