FPT implicit enumeration of active schedules
We consider in this paper the resource constrained scheduling problem with release times and deadlines. We develop an original dynamic programming algorithm generating a compact representation of all feasible active schedules for the decision problem inspired from classical branch-and-bound approach...
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| Vydáno v: | Discrete Applied Mathematics Ročník 376; s. 235 - 250 |
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15.12.2025
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| Abstract | We consider in this paper the resource constrained scheduling problem with release times and deadlines. We develop an original dynamic programming algorithm generating a compact representation of all feasible active schedules for the decision problem inspired from classical branch-and-bound approaches with no time windows. This algorithm is proved to be fixed-parameter tractable (FPT in short) parameterized by the maximum number of jobs overlapping following time windows and the maximum processing time. New dominance rules are also presented to improve the time complexity of our algorithm. Lastly, we also develop an enhanced version of our algorithm to optimize any regular separable objective function. It is shown that this new version of our algorithm has the same time complexity and hence is FPT with the relevant two parameters.
•A generic resource constrained scheduling problem with time windows is introduced.•Fixed-parameter tractable (FPT) algorithm is proposed to generate active schedules.•The FPT algorithm is enhanced to optimize regular objective functions. |
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| AbstractList | We consider in this paper the resource constrained scheduling problem with release times and deadlines. We develop an original dynamic programming algorithm generating a compact representation of all feasible active schedules for the decision problem inspired from classical branch-and-bound approaches with no time windows. This algorithm is proved to be fixed-parameter tractable (FPT in short) parameterized by the maximum number of jobs overlapping following time windows and the maximum processing time. New dominance rules are also presented to improve the time complexity of our algorithm. Lastly, we also develop an enhanced version of our algorithm to optimize any regular separable objective function. It is shown that this new version of our algorithm has the same time complexity and hence is FPT with the relevant two parameters.
•A generic resource constrained scheduling problem with time windows is introduced.•Fixed-parameter tractable (FPT) algorithm is proposed to generate active schedules.•The FPT algorithm is enhanced to optimize regular objective functions. We consider in this paper the resource constrained scheduling problem with release times and deadlines. We develop an original dynamic programming algorithm generating a compact representation of all feasible active schedules for the decision problem inspired from classical branch-and-bound approaches with no time windows. This algorithm is proved to be fixed-parameter tractable (FPT in short) parameterized by the maximum number of jobs overlapping following time windows and the maximum processing time. New dominance rules are also presented to improve the time complexity of our algorithm. Lastly, we also develop an enhanced version of our algorithm to optimize any regular separable objective function. It is shown that this new version of our algorithm has the same time complexity and hence is FPT with the relevant two parameters. |
| Author | Hanen, Claire Tarhan, İstenç Kordon, Alix Munier Carlier, Jacques Jouglet, Antoine |
| Author_xml | – sequence: 1 givenname: İstenç orcidid: 0000-0002-1632-884X surname: Tarhan fullname: Tarhan, İstenç email: istenc.tarhan@ucd.ie organization: Sorbonne Université, CNRS, LIP6 Paris, F-75005, France – sequence: 2 givenname: Claire surname: Hanen fullname: Hanen, Claire email: claire.hanen@lip6.fr organization: Sorbonne Université, CNRS, LIP6 Paris, F-75005, France – sequence: 3 givenname: Alix Munier surname: Kordon fullname: Kordon, Alix Munier email: alix.munier@lip6.fr organization: Sorbonne Université, CNRS, LIP6 Paris, F-75005, France – sequence: 4 givenname: Jacques surname: Carlier fullname: Carlier, Jacques email: jacques.carlier@hds.utc.fr organization: UTC, Heudiasyc Compiègne, 60200, France – sequence: 5 givenname: Antoine surname: Jouglet fullname: Jouglet, Antoine email: antoine.jouglet@hds.utc.fr organization: UTC, Heudiasyc Compiègne, 60200, France |
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| Cites_doi | 10.1137/0204035 10.1016/0377-2217(93)90185-P 10.1287/mnsc.38.12.1803 10.1016/j.dam.2020.11.024 10.1016/S0377-2217(98)00204-5 10.1016/j.cor.2014.04.018 10.1287/mnsc.46.10.1365.12272 10.1287/opre.18.2.263 10.1007/s00291-016-0435-1 10.1007/s10951-018-0578-9 10.1287/mnsc.44.5.714 10.1016/S0377-2217(97)00348-2 10.1287/mnsc.46.5.710.12044 10.1016/0377-2217(93)E0294-8 10.1007/978-3-031-39698-4_10 10.1016/j.asoc.2017.08.033 10.1016/0377-2217(95)00357-6 |
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| Keywords | Scheduling Active schedules Fixed parameter tractable algorithm Parameterized complexity |
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| Title | FPT implicit enumeration of active schedules |
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