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Parameterized Complexity of a Parallel Machine Scheduling Problem

Authors Maher Mallem , Claire Hanen , Alix Munier-Kordon

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Maher Mallem
  • Sorbonne Université, CNRS, LIP6, F-75005 Paris, France
Claire Hanen
  • Sorbonne Université, CNRS, LIP6, F-75005 Paris, France
  • Université Paris Nanterre, UPL, 92000 Nanterre, France
Alix Munier-Kordon
  • Sorbonne Université, CNRS, LIP6, F-75005 Paris, France

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Maher Mallem, Claire Hanen, and Alix Munier-Kordon. Parameterized Complexity of a Parallel Machine Scheduling Problem. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 21:1-21:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.IPEC.2022.21

Abstract

In this paper we consider the parameterized complexity of two versions of a parallel machine scheduling problem with precedence delays, unit processing times and time windows. In the first version - with exact delays - we assume that the delay between two jobs must be exactly respected, whereas in the second version - with minimum delays - the delay between two jobs is a lower bound on the time between them. Two parameters are considered for this analysis: the pathwidth of the interval graph induced by the time windows and the maximum precedence delay value. We prove that our problems are para-NP-complete with respect to any of the two parameters and fixed-parameter tractable parameterized by the pair of parameters.

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
Keywords
  • parameterized complexity
  • scheduling
  • precedence delays
  • pathwidth
  • chains
  • parallel processors

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References

  1. Robert Baart, Mathijs de Weerdt, and Lei He. Single-machine scheduling with release times, deadlines, setup times, and rejection. European Journal of Operational Research, 291(2):629-639, 2021. Google Scholar
  2. S. Bessy and R. Giroudeau. Parameterized complexity of a coupled-task scheduling problem. Journal of Scheduling, 22(3):305-313, June 2019. URL: https://doi.org/10.1007/s10951-018-0581-1.
  3. Hans L Bodlaender and Michael R Fellows. W[2]-hardness of precedence constrained k-processor scheduling. Operations Research Letters, 18(2):93-97, 1995. Google Scholar
  4. Hans L Bodlaender and Marieke van der Wegen. Parameterized complexity of scheduling chains of jobs with delays. In 15th International Symposium on Parameterized and Exact Computation (IPEC), 2020. Google Scholar
  5. P. Brucker, M.R. Garey, and D.S. Johnson. Scheduling equal-length tasks under treelike precedence constraints to minimize maximum lateness. Math. Oper. Res., 2(3):275-284, 1977. Google Scholar
  6. R. Downey and M. Fellows. Parameterized complexity. Springer, 1999. Google Scholar
  7. Rodney G Downey, Michael R Fellows, and Kenneth W Regan. Descriptive complexity and the W hierarchy. In Proof Complexity and Feasible Arithmetics, pages 119-134, 1996. Google Scholar
  8. Jianzhong Du, Joseph YT Leung, and Gilbert H Young. Scheduling chain-structured tasks to minimize makespan and mean flow time. Information and Computation, 92(2):219-236, 1991. Google Scholar
  9. J. Flum and M. Grohe. Parameterized complexity theory. Springer, 1998. Google Scholar
  10. M.R. Garey, D.S. Johnson, R.E. Tarjan, and M. Yannakakis. Scheduling opposing forests. SIAM Journal on Algebraic Discrete Methods, 4(1):72-93, 1983. Google Scholar
  11. Ronald Lewis Graham, Eugene Leighton Lawler, Jan Karel Lenstra, and AHG Rinnooy Kan. Optimization and approximation in deterministic sequencing and scheduling: a survey. In Annals of discrete mathematics, volume 5, pages 287-326. Elsevier, 1979. Google Scholar
  12. Claire Hanen and Alix Munier-Kordon. Fixed-Parameter tractability of scheduling dependent typed tasks subject to release times and deadlines. Submitted, 2021. Google Scholar
  13. Richard M Karp. Reducibility among combinatorial problems. In Complexity of computer computations, pages 85-103. Springer, 1972. Google Scholar
  14. J.K. Lenstra and A.H.G. Rinnooy Kan. Complexity of scheduling under precedence constraints. Oper. Res., 26(1):22-35, 1978. Google Scholar
  15. Matthias Mnich and René van Bevern. Parameterized complexity of machine scheduling: 15 open problems. Computers & Operations Research, 100:254-261, December 2018. URL: https://doi.org/10.1016/j.cor.2018.07.020.
  16. Alix Munier Kordon. A fixed-parameter algorithm for scheduling unit dependent tasks on parallel machines with time windows. Discrete Applied Mathematics, 290:1-6, 2021. Google Scholar
  17. Alex J Orman and Chris N Potts. On the complexity of coupled-task scheduling. Discrete Applied Mathematics, 72(1-2):141-154, 1997. Google Scholar
  18. Linus Schrage. Solving resource-constrained network problems by implicit enumeration - nonpreemptive case. Operations Research, 18(2):263-278, 1970. Google Scholar
  19. J. D. Ullman. NP-complete scheduling problems. Journal of Computer and System sciences, 1975. URL: https://core.ac.uk/reader/82723490.
  20. René van Bevern, Robert Bredereck, Laurent Bulteau, Christian Komusiewicz, Nimrod Talmon, and Gerhard J. Woeginger. Precedence-constrained scheduling problems parameterized by partial order width. In Yury Kochetov, Michael Khachay, Vladimir Beresnev, Evgeni Nurminski, and Panos Pardalos, editors, Discrete Optimization and Operations Research, pages 105-120, Cham, 2016. Springer International Publishing. Google Scholar
  21. René van Bevern, Andrey Melnikov, Pavel V. Smirnov, and Oxana Yu. Tsidulko. On data reduction for dynamic vector bin packing. CoRR, abs/2205.08769, 2022. URL: https://doi.org/10.48550/arXiv.2205.08769.
  22. Wenci Yu, Han Hoogeveen, and Jan Karel Lenstra. Minimizing Makespan in a Two-Machine Flow Shop with Delays and Unit-Time Operations is NP-Hard. Journal of Scheduling, 7(5):333-348, September 2004. URL: https://doi.org/10.1023/B:JOSH.0000036858.59787.c2.
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