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DOI: 10.4230/OASIcs.ATMOS.2024.5

Balanced Assignments of Periodic Tasks

Authors: Héloïse Gachet and Frédéric Meunier

Published in: OASIcs, Volume 123, 24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)

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.

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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)

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@InProceedings{gachet_et_al:OASIcs.ATMOS.2024.5,
  author =	{Gachet, H\'{e}lo\"{i}se and Meunier, Fr\'{e}d\'{e}ric},
  title =	{{Balanced Assignments of Periodic Tasks}},
  booktitle =	{24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)},
  pages =	{5:1--5:12},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-350-8},
  ISSN =	{2190-6807},
  year =	{2024},
  volume =	{123},
  editor =	{Bouman, Paul C. and Kontogiannis, Spyros C.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2024.5},
  URN =		{urn:nbn:de:0030-drops-211938},
  doi =		{10.4230/OASIcs.ATMOS.2024.5},
  annote =	{Keywords: Fair schedule, Eulerian digraph, Markov chain, interval graph}
}

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DOI: 10.4230/OASIcs.ATMOS.2014.34

Online Train Shunting

Authors: Vianney Boeuf and Frédéric Meunier

Published in: OASIcs, Volume 42, 14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2014)

Abstract

At the occasion of ATMOS 2012, Tim Nonner and Alexander Souza defined a new train shunting problem that can roughly be described as follows. We are given a train visiting stations in a given order and cars located at some source stations. Each car has a target station. During the trip of the train, the cars are added to the train at their source stations and removed from it at their target stations. An addition or a removal of a car in the strict interior of the train incurs a cost higher than when the operation is performed at the end of the train. The problem consists in minimizing the total cost, and thus, at each source station of a car, the position the car takes in the train must be carefully decided. Among other results, Nonner and Souza showed that this problem is polynomially solvable by reducing the problem to the computation of a minimum independent set in a bipartite graph. They worked in the offline setting, i.e. the sources and the targets of all cars are known before the trip of the train starts. We study the online version of the problem, in which cars become known at their source stations. We derive a 2-competitive algorithm and prove than no better ratios are achievable. Other related questions are also addressed.

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Vianney Boeuf and Frédéric Meunier. Online Train Shunting. In 14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 42, pp. 34-45, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{boeuf_et_al:OASIcs.ATMOS.2014.34,
  author =	{Boeuf, Vianney and Meunier, Fr\'{e}d\'{e}ric},
  title =	{{Online Train Shunting}},
  booktitle =	{14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{34--45},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-75-0},
  ISSN =	{2190-6807},
  year =	{2014},
  volume =	{42},
  editor =	{Funke, Stefan and Mihal\'{a}k, Mat\'{u}s},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2014.34},
  URN =		{urn:nbn:de:0030-drops-47512},
  doi =		{10.4230/OASIcs.ATMOS.2014.34},
  annote =	{Keywords: Bipartite graph, competitive analysis, online algorithm, train shunting problem, vertex cover}
}

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Balanced Assignments of Periodic Tasks

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Online Train Shunting

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