Approximation Algorithms for Multiprocessor Scheduling with Testing to Minimize the Total Job Completion Time
In offline scheduling models, jobs are given with their exact processing times. In their online counterparts, jobs arrive in sequence together with their processing times and the scheduler makes irrevocable decisions on how to execute each of them upon its arrival. We consider a semi-online variant...
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| Published in | Algorithmica Vol. 86; no. 5; pp. 1400 - 1427 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.05.2024
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0178-4617 1432-0541 |
| DOI | 10.1007/s00453-023-01198-w |
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| Abstract | In offline scheduling models, jobs are given with their exact processing times. In their online counterparts, jobs arrive in sequence together with their processing times and the scheduler makes irrevocable decisions on how to execute each of them upon its arrival. We consider a semi-online variant which has equally rich application background, called scheduling with testing, where the exact processing time of a job is revealed only after a required testing operation is finished, or otherwise the job has to be executed for a given possibly over-estimated length of time. For multiprocessor scheduling with testing to minimize the total job completion time, we present several first approximation algorithms with constant competitive ratios for various settings, including a
2
φ
-competitive algorithm for the non-preemptive general testing case and a
(
0.0382
+
2.7925
(
1
-
1
2
m
)
)
-competitive randomized algorithm, when the number of machines
m
≥
37
or otherwise 2.7925-competitive, where
φ
=
(
1
+
5
)
/
2
<
1.6181
is the golden ratio and
m
is the number of machines, a
(
3.5
-
3
2
m
)
-competitive algorithm allowing job preemption when
m
≥
3
or otherwise 3-competitive, and a
(
φ
+
φ
+
1
2
(
1
-
1
m
)
)
-competitive algorithm for the non-preemptive uniform testing case when
m
≥
5
or otherwise
(
φ
+
1
)
-competitive. Our results improve three previous best approximation algorithms for the single machine scheduling with testing problems, respectively. |
|---|---|
| AbstractList | In offline scheduling models, jobs are given with their exact processing times. In their online counterparts, jobs arrive in sequence together with their processing times and the scheduler makes irrevocable decisions on how to execute each of them upon its arrival. We consider a semi-online variant which has equally rich application background, called scheduling with testing, where the exact processing time of a job is revealed only after a required testing operation is finished, or otherwise the job has to be executed for a given possibly over-estimated length of time. For multiprocessor scheduling with testing to minimize the total job completion time, we present several first approximation algorithms with constant competitive ratios for various settings, including a 2φ-competitive algorithm for the non-preemptive general testing case and a (0.0382+2.7925(1-12m))-competitive randomized algorithm, when the number of machines m≥37 or otherwise 2.7925-competitive, where φ=(1+5)/2<1.6181 is the golden ratio and m is the number of machines, a (3.5-32m)-competitive algorithm allowing job preemption when m≥3 or otherwise 3-competitive, and a (φ+φ+12(1-1m))-competitive algorithm for the non-preemptive uniform testing case when m≥5 or otherwise (φ+1)-competitive. Our results improve three previous best approximation algorithms for the single machine scheduling with testing problems, respectively. In offline scheduling models, jobs are given with their exact processing times. In their online counterparts, jobs arrive in sequence together with their processing times and the scheduler makes irrevocable decisions on how to execute each of them upon its arrival. We consider a semi-online variant which has equally rich application background, called scheduling with testing, where the exact processing time of a job is revealed only after a required testing operation is finished, or otherwise the job has to be executed for a given possibly over-estimated length of time. For multiprocessor scheduling with testing to minimize the total job completion time, we present several first approximation algorithms with constant competitive ratios for various settings, including a 2 φ -competitive algorithm for the non-preemptive general testing case and a ( 0.0382 + 2.7925 ( 1 - 1 2 m ) ) -competitive randomized algorithm, when the number of machines m ≥ 37 or otherwise 2.7925-competitive, where φ = ( 1 + 5 ) / 2 < 1.6181 is the golden ratio and m is the number of machines, a ( 3.5 - 3 2 m ) -competitive algorithm allowing job preemption when m ≥ 3 or otherwise 3-competitive, and a ( φ + φ + 1 2 ( 1 - 1 m ) ) -competitive algorithm for the non-preemptive uniform testing case when m ≥ 5 or otherwise ( φ + 1 ) -competitive. Our results improve three previous best approximation algorithms for the single machine scheduling with testing problems, respectively. |
| Author | Hayashi, Kuniteru Gong, Mingyang Chen, Zhi-Zhong |
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| Cites_doi | 10.1016/j.apm.2021.12.020 10.1002/j.1538-7305.1966.tb01709.x 10.1007/978-3-319-26580-3 10.1007/s10878-022-00865-y 10.1007/978-3-030-80879-2_9 10.1007/978-3-030-83508-8_3 10.1007/978-3-030-97099-4_5 10.1145/375551.375577 10.1145/3544979.3544993 10.1287/mnsc.11.2.268 10.1007/s00453-020-00742-2 10.1007/s00224-004-1180-4 10.1145/103418.103449 10.1287/mnsc.2017.2973 10.1137/S0097539701395668 |
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| Keywords | Multiprocessor Scheduling Scheduling with testing Total job completion time Approximation algorithm |
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| References | ConwayRWMaxwellWLMillerLWTheory of Scheduling1967ReadingAddison-Wesley Co. Kahan, S.: A model for data in motion. In: Proceedings of the Twenty-Third Annual ACM Symposium on Theory of Computing (STOC’91), pp. 265–277 (1991) LeviRMagnantiTShaposhnikYScheduling with testingManag. Sci.20196577679310.1287/mnsc.2017.2973 BruceRHoffmannMKrizancDRamanREfficient update strategies for geometric computing with uncertaintyTheory Comput. Syst.200538411423214011810.1007/s00224-004-1180-4 GongMGoebelRLinGMiyanoEImproved approximation algorithms for non-preemptive multiprocessor scheduling with testingJ. Comb. Optim.202244877893445873010.1007/s10878-022-00865-y Olston, C., Widom, J.: Offering a precision-performance tradeoff for aggregation queries over replicated data. In: The 26th International Conference on Very Large Data Bases (VLDB 2000), pp. 144–155 (2000) Gupta, M., Sabharwal, Y., Sen, S.: The update complexity of selection and related problems. In: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011), LIPIcs 13, pp. 325–338 (2011) GareyMRJohnsonDSComputers and Intractability: A Guide to the Theory of NP-Completeness1979San FranciscoW. H. Freeman and Company PinedoMScheduling: Theory, Algorithm and Systems20165New YorkSpringer10.1007/978-3-319-26580-3 Dürr, C., Erlebach, T., Megow, N., Meißner, J.: Scheduling with explorable uncertainty. In: Proceedings of ITCS 2018, LIPIcs 94, pp. 30:1–30:14 (2018) DufosséFDürrCNadalNTrystramDVásquezÓCScheduling with a processing time oracleAppl. Math. Model.2022104701720435765110.1016/j.apm.2021.12.020 GrahamRLBounds for certain multiprocessing anomaliesBell Labs Tech. J.1966451563158110.1002/j.1538-7305.1966.tb01709.x Albers, S., Eckl, A.: Scheduling with testing on multiple identical parallel machines. In: Proceedings of WADS 2021, LNCS 12808, pp. 29–42 (2021). A full version appears as arXiv:2105.02052 in Computing Research Repository DwibedyDMohantyROnline list scheduling for makespan minimization: a review of the state-of-the-art results, research challenges and open problemsACM SIGACT News20225384105447734110.1145/3544979.3544993 FederTMotwaniRPanigrahyROlstonCWidomJComputing the median with uncertaintySIAM J. Comput.200332538547196940310.1137/S0097539701395668 EastmanWLEvenSIsaacsIMBounds for the optimal scheduling of n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document} jobs on m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m$$\end{document} processorsManag. Sci.19641126827917354710.1287/mnsc.11.2.268 Gong, M., Lin, G.: Improved approximation algorithms for multiprocessor scheduling with testing. In: Proceedings of FAW 2021, LNCS 12874, pp. 65–77 (2021) Albers, S., Eckl, A.: Explorable uncertainty in scheduling with non-uniform testing times. In: Proceedings of WAOA 2020, LNCS 12806, pp. 127–142 (2020). A full version appears as arXiv:2009.13316 in Computing Research Repository Khanna, S., Tan, W.C.: On computing functions with uncertainty. In: Proceedings of the 20th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems (PODS 2001), pp. 171–182 (2001) DürrCErlebachTMegowNMeißnerJAn adversarial model for scheduling with testingAlgorithmica20208236303675416904510.1007/s00453-020-00742-2 RW Conway (1198_CR4) 1967 M Pinedo (1198_CR20) 2016 D Dwibedy (1198_CR8) 2022; 53 RL Graham (1198_CR14) 1966; 45 M Gong (1198_CR12) 2022; 44 C Dürr (1198_CR7) 2020; 82 1198_CR19 T Feder (1198_CR10) 2003; 32 1198_CR17 1198_CR16 1198_CR15 1198_CR13 1198_CR1 1198_CR2 R Bruce (1198_CR3) 2005; 38 MR Garey (1198_CR11) 1979 R Levi (1198_CR18) 2019; 65 1198_CR6 WL Eastman (1198_CR9) 1964; 11 F Dufossé (1198_CR5) 2022; 104 |
| References_xml | – reference: GareyMRJohnsonDSComputers and Intractability: A Guide to the Theory of NP-Completeness1979San FranciscoW. H. Freeman and Company – reference: BruceRHoffmannMKrizancDRamanREfficient update strategies for geometric computing with uncertaintyTheory Comput. Syst.200538411423214011810.1007/s00224-004-1180-4 – reference: GrahamRLBounds for certain multiprocessing anomaliesBell Labs Tech. J.1966451563158110.1002/j.1538-7305.1966.tb01709.x – reference: Olston, C., Widom, J.: Offering a precision-performance tradeoff for aggregation queries over replicated data. In: The 26th International Conference on Very Large Data Bases (VLDB 2000), pp. 144–155 (2000) – reference: Albers, S., Eckl, A.: Explorable uncertainty in scheduling with non-uniform testing times. In: Proceedings of WAOA 2020, LNCS 12806, pp. 127–142 (2020). A full version appears as arXiv:2009.13316 in Computing Research Repository – reference: Khanna, S., Tan, W.C.: On computing functions with uncertainty. In: Proceedings of the 20th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems (PODS 2001), pp. 171–182 (2001) – reference: DwibedyDMohantyROnline list scheduling for makespan minimization: a review of the state-of-the-art results, research challenges and open problemsACM SIGACT News20225384105447734110.1145/3544979.3544993 – reference: Gong, M., Lin, G.: Improved approximation algorithms for multiprocessor scheduling with testing. In: Proceedings of FAW 2021, LNCS 12874, pp. 65–77 (2021) – reference: EastmanWLEvenSIsaacsIMBounds for the optimal scheduling of n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document} jobs on m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m$$\end{document} processorsManag. Sci.19641126827917354710.1287/mnsc.11.2.268 – reference: GongMGoebelRLinGMiyanoEImproved approximation algorithms for non-preemptive multiprocessor scheduling with testingJ. Comb. Optim.202244877893445873010.1007/s10878-022-00865-y – reference: ConwayRWMaxwellWLMillerLWTheory of Scheduling1967ReadingAddison-Wesley Co. – reference: FederTMotwaniRPanigrahyROlstonCWidomJComputing the median with uncertaintySIAM J. Comput.200332538547196940310.1137/S0097539701395668 – reference: Albers, S., Eckl, A.: Scheduling with testing on multiple identical parallel machines. In: Proceedings of WADS 2021, LNCS 12808, pp. 29–42 (2021). A full version appears as arXiv:2105.02052 in Computing Research Repository – reference: DürrCErlebachTMegowNMeißnerJAn adversarial model for scheduling with testingAlgorithmica20208236303675416904510.1007/s00453-020-00742-2 – reference: PinedoMScheduling: Theory, Algorithm and Systems20165New YorkSpringer10.1007/978-3-319-26580-3 – reference: Dürr, C., Erlebach, T., Megow, N., Meißner, J.: Scheduling with explorable uncertainty. In: Proceedings of ITCS 2018, LIPIcs 94, pp. 30:1–30:14 (2018) – reference: Kahan, S.: A model for data in motion. In: Proceedings of the Twenty-Third Annual ACM Symposium on Theory of Computing (STOC’91), pp. 265–277 (1991) – reference: LeviRMagnantiTShaposhnikYScheduling with testingManag. Sci.20196577679310.1287/mnsc.2017.2973 – reference: DufosséFDürrCNadalNTrystramDVásquezÓCScheduling with a processing time oracleAppl. Math. Model.2022104701720435765110.1016/j.apm.2021.12.020 – reference: Gupta, M., Sabharwal, Y., Sen, S.: The update complexity of selection and related problems. In: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011), LIPIcs 13, pp. 325–338 (2011) – volume: 104 start-page: 701 year: 2022 ident: 1198_CR5 publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2021.12.020 – volume: 45 start-page: 1563 year: 1966 ident: 1198_CR14 publication-title: Bell Labs Tech. J. doi: 10.1002/j.1538-7305.1966.tb01709.x – volume-title: Scheduling: Theory, Algorithm and Systems year: 2016 ident: 1198_CR20 doi: 10.1007/978-3-319-26580-3 – volume: 44 start-page: 877 year: 2022 ident: 1198_CR12 publication-title: J. Comb. Optim. doi: 10.1007/s10878-022-00865-y – ident: 1198_CR1 doi: 10.1007/978-3-030-80879-2_9 – ident: 1198_CR2 doi: 10.1007/978-3-030-83508-8_3 – ident: 1198_CR15 – ident: 1198_CR13 doi: 10.1007/978-3-030-97099-4_5 – ident: 1198_CR17 doi: 10.1145/375551.375577 – volume: 53 start-page: 84 year: 2022 ident: 1198_CR8 publication-title: ACM SIGACT News doi: 10.1145/3544979.3544993 – volume: 11 start-page: 268 year: 1964 ident: 1198_CR9 publication-title: Manag. Sci. doi: 10.1287/mnsc.11.2.268 – volume: 82 start-page: 3630 year: 2020 ident: 1198_CR7 publication-title: Algorithmica doi: 10.1007/s00453-020-00742-2 – volume: 38 start-page: 411 year: 2005 ident: 1198_CR3 publication-title: Theory Comput. Syst. doi: 10.1007/s00224-004-1180-4 – ident: 1198_CR16 doi: 10.1145/103418.103449 – volume: 65 start-page: 776 year: 2019 ident: 1198_CR18 publication-title: Manag. Sci. doi: 10.1287/mnsc.2017.2973 – ident: 1198_CR19 – volume: 32 start-page: 538 year: 2003 ident: 1198_CR10 publication-title: SIAM J. Comput. doi: 10.1137/S0097539701395668 – volume-title: Theory of Scheduling year: 1967 ident: 1198_CR4 – ident: 1198_CR6 – volume-title: Computers and Intractability: A Guide to the Theory of NP-Completeness year: 1979 ident: 1198_CR11 |
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| SubjectTerms | Algorithm Analysis and Problem Complexity Algorithms Approximation Competition Completion time Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Mathematical analysis Mathematics of Computing Multiprocessing Preempting Scheduling Theory of Computation |
| Title | Approximation Algorithms for Multiprocessor Scheduling with Testing to Minimize the Total Job Completion Time |
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