Sublinear time approximation schemes for makespan minimization on parallel machines

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...

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Bibliographic Details
Published in:Mathematical methods of operations research (Heidelberg, Germany) Vol. 101; no. 3; pp. 507 - 528
Main Authors: Fu, Bin, Huo, Yumei, Zhao, Hairong
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2025
Springer Nature B.V
Subjects:
Algorithms
Approximation
Business and Management
Calculus of Variations and Optimal Control; Optimization
Manufacturers
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Original Article
Precedence constraints
Random sampling
Scheduling
Parallel machine
Sublinear time algorithms
Precedence constraints
Makespan minimization
Uniform sampling
ISSN:1432-2994, 1432-5217
Online Access:Get full text
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Summary: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 . We then extend our algorithm to the more general problem where the largest jobs have processing times that differ by no more than c factor for some constant , . When , our algorithm is a randomized -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.
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ISSN:1432-2994
1432-5217
DOI:10.1007/s00186-025-00898-z