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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Veröffentlicht in:	Mathematical methods of operations research (Heidelberg, Germany) Jg. 101; H. 3; S. 507 - 528
Hauptverfasser:	Fu, Bin, Huo, Yumei, Zhao, Hairong
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2025 Springer Nature B.V
Schlagworte:	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
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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 . 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.
AbstractList	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. 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.
Author	Huo, Yumei Zhao, Hairong Fu, Bin
Author_xml	– sequence: 1 givenname: Bin surname: Fu fullname: Fu, Bin organization: Department of Computer Science, University of Texas Rio Grande Valley – sequence: 2 givenname: Yumei orcidid: 0000-0003-3550-8843 surname: Huo fullname: Huo, Yumei email: yumei.huo@csi.cuny.edu organization: Department of Computer Science, College of Staten Island, CUNY – sequence: 3 givenname: Hairong surname: Zhao fullname: Zhao, Hairong organization: Department of Computer Science, Purdue University Northwest
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Cites_doi	10.1007/11830924_34 10.1016/0196-6774(84)90039-7 10.1017/CBO9780511814075 10.1109/FOCS.2009.23 10.1137/S0097539702403244 10.1002/j.1538-7305.1966.tb01709.x 10.1145/1007352.1007386 10.1145/321921.321934 10.1007/3-540-45123-4_10 10.1007/s10878-007-9092-2 10.1016/S0022-0000(75)80008-0 10.1007/s10951-017-0519-z 10.1137/100810502 10.1137/16M1105049 10.1145/7531.7535 10.1287/opre.26.1.22 10.1137/S0097539703435297 10.1137/S0097539704447304 10.1137/S009753970444572X 10.1007/BF00288685 10.1145/285055.285060 10.1137/0117039
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SubjectTerms	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
Title	Sublinear time approximation schemes for makespan minimization on parallel machines
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