OASIcs.ATMOS.2024.5.pdf
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Balanced Assignments of Periodic Tasks
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Frédéric Meunier 
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24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)
Series: Open Access Series in Informatics (OASIcs)
Conference: Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-10-07
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Acknowledgements
The authors are also grateful to Jean-François Delmas for pointing out the situation of "normal numbers," whose existence status shares some similarity with that of balanced feasible assignments; see Section 4.1.
Cite AsGet BibTex
Héloïse Gachet and Frédéric Meunier. Balanced Assignments of Periodic Tasks. In 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024). Open Access Series in Informatics (OASIcs), Volume 123, pp. 5:1-5:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/OASIcs.ATMOS.2024.5
https://doi.org/10.4230/OASIcs.ATMOS.2024.5
Abstract
This work deals with a problem of assigning periodic tasks to employees in such a way that each employee performs each task with the same frequency in the long term. The motivation comes from a collaboration with the main French railway company, the SNCF. An almost complete solution is provided under the form of a necessary and sufficient condition that can be checked in polynomial time. A complementary discussion about possible extensions is also proposed.
Subject Classification
ACM Subject Classification
- Mathematics of computing → Graph algorithms
- Applied computing → Transportation
Keywords
- Fair schedule
- Eulerian digraph
- Markov chain
- interval graph
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References
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