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2021 | OriginalPaper | Buchkapitel

Two Deadline Reduction Algorithms for Scheduling Dependent Tasks on Parallel Processors

verfasst von : Claire Hanen, Alix Munier Kordon, Theo Pedersen

Erschienen in: Integration of Constraint Programming, Artificial Intelligence, and Operations Research

Verlag: Springer International Publishing

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Abstract

This paper proposes two deadline adjustment techniques for scheduling non preemptive tasks subject to precedence relations, release dates and deadlines on a limited number of processors. This decision problem is denoted by \(P\vert prec, r_i, d_i\vert \star \) in standard notations. The first technique is an extension of the Garey and Johnson algorithm that integrates precedence relations in energetic reasoning. The second one is an extension of the Leung, Palem and Pnueli algorithm that builds iteratively relaxed preemptive schedules to adjust deadlines.
The implementation of the two classes of algorithms is discussed and compared on randomly generated instances. We show that the adjustments obtained are slightly different but equivalent using several metrics. However, the time performance of the extended Leung, Palem and Pnueli algorithm is much better than that of the extended Garey and Johnson ones.

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Literatur
1.
Zurück zum Zitat Baptiste, P., Le Pape, C., Nuijten, W.: Satisfiability tests and time-bound adjustments for cumulative scheduling problems. Ann. Oper. Res. 92, 305–333 (1999)MathSciNetCrossRef Baptiste, P., Le Pape, C., Nuijten, W.: Satisfiability tests and time-bound adjustments for cumulative scheduling problems. Ann. Oper. Res. 92, 305–333 (1999)MathSciNetCrossRef
2.
Zurück zum Zitat Bellenguez-Morineau, O.: Methods to solve multi-skill project scheduling problem. 4OR 6(1), 85–88 (2008) Bellenguez-Morineau, O.: Methods to solve multi-skill project scheduling problem. 4OR 6(1), 85–88 (2008)
3.
Zurück zum Zitat Bonifas, N.: A \(\cal{O}(n^2 \log (n))\) propagation for the energy reasoning. In: Congrès ROADEF, February 2016 Bonifas, N.: A \(\cal{O}(n^2 \log (n))\) propagation for the energy reasoning. In: Congrès ROADEF, February 2016
5.
Zurück zum Zitat Carlier, J., Latapie, B.: Une méthode arborescente pour résoudre les problèmes cumulatifs. RAIRO - Oper. Res. Rech. Opérationnelle 25(3), 311–340 (1991)CrossRef Carlier, J., Latapie, B.: Une méthode arborescente pour résoudre les problèmes cumulatifs. RAIRO - Oper. Res. Rech. Opérationnelle 25(3), 311–340 (1991)CrossRef
6.
Zurück zum Zitat Carlier, J., Pinson, E., Sahli, A., Jouglet, A.: An \(\cal{O}(n^2)\) algorithm for time-bound adjustments for the cumulative scheduling problem. Eur. J. Oper. Res. 286(2), 468–476 (2020) Carlier, J., Pinson, E., Sahli, A., Jouglet, A.: An \(\cal{O}(n^2)\) algorithm for time-bound adjustments for the cumulative scheduling problem. Eur. J. Oper. Res. 286(2), 468–476 (2020)
7.
Zurück zum Zitat Carlier, J., Pinson, E., Sahli, A., Jouglet, A.: Comparison of three classical lower bounds for the cumulative scheduling problem. (submitted) (2021) Carlier, J., Pinson, E., Sahli, A., Jouglet, A.: Comparison of three classical lower bounds for the cumulative scheduling problem. (submitted) (2021)
8.
Zurück zum Zitat Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, Third Edition. The MIT Press, 3rd edn., Cambridge (2009) Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, Third Edition. The MIT Press, 3rd edn., Cambridge (2009)
10.
Zurück zum Zitat Edmonds, J., Karp, R.M.: Theoretical improvements in algorithmic efficiency for network flow problems. J. ACM (JACM) 19(2), 248–264 (1972)CrossRef Edmonds, J., Karp, R.M.: Theoretical improvements in algorithmic efficiency for network flow problems. J. ACM (JACM) 19(2), 248–264 (1972)CrossRef
11.
Zurück zum Zitat Garey, M.R., Johnson, D.S.: Two-processor scheduling with start-time and deadlines. SIAM J. Comput. 6, 416–426 (1977)MathSciNetCrossRef Garey, M.R., Johnson, D.S.: Two-processor scheduling with start-time and deadlines. SIAM J. Comput. 6, 416–426 (1977)MathSciNetCrossRef
12.
Zurück zum Zitat Goldberg, A.V., Tarjan, R.E.: A new approach to the maximum-flow problem. J. ACM (JACM) 35(4), 921–940 (1988)MathSciNetCrossRef Goldberg, A.V., Tarjan, R.E.: A new approach to the maximum-flow problem. J. ACM (JACM) 35(4), 921–940 (1988)MathSciNetCrossRef
13.
Zurück zum Zitat Goldberg, A.V., Tarjan, R.E.: Efficient maximum flow algorithms. Commun. ACM 57(8), 82–89 (2014)CrossRef Goldberg, A.V., Tarjan, R.E.: Efficient maximum flow algorithms. Commun. ACM 57(8), 82–89 (2014)CrossRef
14.
Zurück zum Zitat Graham, R., Lawler, E., Lenstra, J., Kan, A.: Optimization and approximation in deterministic sequencing and scheduling: a survey. In: Hammer, P., Johnson, E., Korte, B. (eds.) Discrete Optimization II, Annals of Discrete Mathematics, vol. 5, pp. 287–326. Elsevier (1979) Graham, R., Lawler, E., Lenstra, J., Kan, A.: Optimization and approximation in deterministic sequencing and scheduling: a survey. In: Hammer, P., Johnson, E., Korte, B. (eds.) Discrete Optimization II, Annals of Discrete Mathematics, vol. 5, pp. 287–326. Elsevier (1979)
15.
Zurück zum Zitat Hanen, C., Munier Kordon, A.: Two deadline reduction algorithms for scheduling dependent typed-tasks systems. In: ROADEF conference (2020) Hanen, C., Munier Kordon, A.: Two deadline reduction algorithms for scheduling dependent typed-tasks systems. In: ROADEF conference (2020)
17.
Zurück zum Zitat Hanen, C., Zinder, Y.: The worst-case analysis of the Garey-Johnson algorithm. J. Sched. 12(4), 389–400 (2009)MathSciNetCrossRef Hanen, C., Zinder, Y.: The worst-case analysis of the Garey-Johnson algorithm. J. Sched. 12(4), 389–400 (2009)MathSciNetCrossRef
18.
Zurück zum Zitat Haouari, M., Kooli, A., Néron, E.: Enhanced energetic reasoning-based lower bounds for the resource constrained project scheduling problem. Comput. Oper. Res. 39(5), 1187–1194 (2012)MathSciNetCrossRef Haouari, M., Kooli, A., Néron, E.: Enhanced energetic reasoning-based lower bounds for the resource constrained project scheduling problem. Comput. Oper. Res. 39(5), 1187–1194 (2012)MathSciNetCrossRef
19.
Zurück zum Zitat Haouari, M., Kooli, A., Néron, E., Carlier, J.: A preemptive bound for the resource constrained project scheduling problem. J. Sched. 17(3), 237–248 (2014)MathSciNetCrossRef Haouari, M., Kooli, A., Néron, E., Carlier, J.: A preemptive bound for the resource constrained project scheduling problem. J. Sched. 17(3), 237–248 (2014)MathSciNetCrossRef
20.
Zurück zum Zitat Jackson, J.R.: Scheduling a production line to minimize maximum tardiness. management science research project (1955) Jackson, J.R.: Scheduling a production line to minimize maximum tardiness. management science research project (1955)
21.
Zurück zum Zitat Laborie, P.: Algorithms for propagating resource constraints in AI planning and scheduling: Existing approaches and new results. Artif. Intell. 143(2), 151–188 (2003)MathSciNetCrossRef Laborie, P.: Algorithms for propagating resource constraints in AI planning and scheduling: Existing approaches and new results. Artif. Intell. 143(2), 151–188 (2003)MathSciNetCrossRef
22.
Zurück zum Zitat Laborie, P., Nuijten, W.: Constraint Programming Formulations and propagation Algorithms, chap. 4, pp. 63–72. Wiley, Hoboken (2008) Laborie, P., Nuijten, W.: Constraint Programming Formulations and propagation Algorithms, chap. 4, pp. 63–72. Wiley, Hoboken (2008)
23.
Zurück zum Zitat Leung, A., Palem, K.V., Pnueli, A.: Scheduling time-constrained instructions on pipelined processors. ACM Trans. Program. Lang. Syst. 23, 73–103 (2001)CrossRef Leung, A., Palem, K.V., Pnueli, A.: Scheduling time-constrained instructions on pipelined processors. ACM Trans. Program. Lang. Syst. 23, 73–103 (2001)CrossRef
24.
Zurück zum Zitat Lombardi, M., Milano, M.: Optimal methods for resource allocation and scheduling: a cross-disciplinary survey. Constr. An Int. J. 17(1), 51–85 (2012)MathSciNetCrossRef Lombardi, M., Milano, M.: Optimal methods for resource allocation and scheduling: a cross-disciplinary survey. Constr. An Int. J. 17(1), 51–85 (2012)MathSciNetCrossRef
25.
Zurück zum Zitat Martel, C.: Preemptive scheduling with release times, deadlines, and due times. J. Assoc. Comput. Mach. 29(3), 812–829 (1982)MathSciNetCrossRef Martel, C.: Preemptive scheduling with release times, deadlines, and due times. J. Assoc. Comput. Mach. 29(3), 812–829 (1982)MathSciNetCrossRef
26.
Zurück zum Zitat Munier Kordon, A.: A fixed-parameter algorithm for scheduling unit dependent tasks on parallel machines with time windows. Discret. Appl. Math. 290, 1–6 (2021)MathSciNetCrossRef Munier Kordon, A.: A fixed-parameter algorithm for scheduling unit dependent tasks on parallel machines with time windows. Discret. Appl. Math. 290, 1–6 (2021)MathSciNetCrossRef
Metadaten
Titel
Two Deadline Reduction Algorithms for Scheduling Dependent Tasks on Parallel Processors
verfasst von
Claire Hanen
Alix Munier Kordon
Theo Pedersen
Copyright-Jahr
2021
DOI
https://doi.org/10.1007/978-3-030-78230-6_14

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