Computer Science Faculty Publications and Presentations
Sublinear time approximation schemes for makespan minimization on parallel machines
Document Type
Article
Publication Date
7-15-2025
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 nϵ20c. We then extend our algorithm to the more general problem where the largest αn jobs have processing times that differ by no more than c factor for some constant α, 0< α≤1. When m≤αnϵ20c2, our algorithm is a randomized (1+ϵ)-approximation scheme that runs in sublinear time. We further generalize our algorithms to the scheduling problems with precedence constraints where the precedence graph has a bounded depth h. Our work not only provides an algorithmic solution to the studied scheduling problem under big data environment, but also gives a methodological framework for designing sublinear time approximation algorithms for other scheduling problems.
Recommended Citation
Fu, Bin, Yumei Huo, and Hairong Zhao. "Sublinear time approximation schemes for makespan minimization on parallel machines." Mathematical Methods of Operations Research 101, no. 3 (2025): 507-528. https://doi.org/10.1007/s00186-025-00898-z
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This work is licensed under a Creative Commons Attribution 4.0 International License.
Publication Title
Mathematical Methods of Operations Research
DOI
10.1007/s00186-025-00898-z
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