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Exact algorithms for scheduling programs with shared tasks

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Abstract

We study a scheduling problem where the jobs we have to perform are composed of one or more tasks. If two jobs sharing a non-empty subset of tasks are scheduled on the same machine, then these shared tasks have to be performed only once. This kind of problem is known in the literature under the names of VM-PACKING or PAGINATION. Our objective is to schedule a set of these objects on two parallel identical machines, with the aim of minimizing the makespan. This problem is NP-complete as an extension of the PARTITION problem. In this paper we present three exact algorithms with worst-case time-complexity guarantees, by exploring different branching techniques. Our first algorithm focuses on the relation between jobs sharing one or more symbols in common, whereas the two other algorithms branches on the shared symbols.

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Acknowledgements

This work has been funded by the UNIVERSITE DE LORRAINE and the REGION GRAND-EST (Project: Modélisation, caractérisation et résolution de nouveaux problèmes de pagination, Délibération num 17CP-1391, Date : 13/07/2017). The authors are grateful to the referees for their helpful and constructive remarks and comments, which allowed us to improve the quality of this paper.

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  1. LCOMS, Université de Lorraine, Metz, France

    Imed Kacem, Giorgio Lucarelli & Théo Nazé

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  1. Imed Kacem
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  2. Giorgio Lucarelli
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  3. Théo Nazé
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Correspondence to Théo Nazé.

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A preliminary version has been presented in the WorldCIST Conference. Kacem I, Lucarelli G, Nazé T (2020) Exact algorithms for scheduling programs with shared tasks. In: Trends and innovations in information systems and technologies–Volume 2, WorldCIST 2020, Budva, Montenegro, 7–10 April 2020. Advances in Intelligent Systems and Computing, vol 1160. Springer, pp 435–444.

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Kacem, I., Lucarelli, G. & Nazé, T. Exact algorithms for scheduling programs with shared tasks. J Comb Optim 43, 1602–1627 (2022). https://doi.org/10.1007/s10878-021-00702-8

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  • DOI: https://doi.org/10.1007/s10878-021-00702-8

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