Abstract
We consider in this paper the scheduling problem defined by a set of dependent jobs with release times and deadlines to be processed by identical parallel machines. This problem is denoted by \(P\vert prec,r_i,d_i\vert \star \) in the literature. Starting from an extension of the Branch-and-Bound algorithm of Demeulemeester and Herroelen to take into account release times and deadlines, we build a state graph of which longest paths represent all active schedule. New dominance rules are also proposed.
We establish that our state graph construction algorithm is fixed-parameter tractable. The two parameters are the pathwidth, which corresponds to the maximum number of overlapping jobs time windows and the maximum execution time of a job. The algorithm is experimented on random instances. These experiments show that the pathwidth is also a key factor of the practical complexity of the algorithm.
Supported by EASI project, Sorbonne Universités.
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This work was supported by the EASI project funded by Sorbonne Universités.
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Tarhan, I., Carlier, J., Hanen, C., Jouglet, A., Munier Kordon, A. (2023). Parameterized Analysis of a Dynamic Programming Algorithm for a Parallel Machine Scheduling Problem. In: Cano, J., Dikaiakos, M.D., Papadopoulos, G.A., Pericàs, M., Sakellariou, R. (eds) Euro-Par 2023: Parallel Processing. Euro-Par 2023. Lecture Notes in Computer Science, vol 14100. Springer, Cham. https://doi.org/10.1007/978-3-031-39698-4_10
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