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On the p-Median Polytope and the Directed Odd Cycle Inequalities

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Combinatorial Optimization (ISCO 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12176))

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Abstract

We study the effect of the odd directed cycle inequalities in the description of the polytope associated with the p-median problem. We treat general directed graphs and we characterize all the graphs for which the obvious linear relaxation together with the directed odd cycle inequalities describe the p-median polytope. In a previous work we have shown a similar result for oriented graphs. This result extends the previous work, but its proof depends on the oriented case since it will be the starting point of the proof in this paper.

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References

  1. Baïou, M., Barahona, F.: On the linear relaxation of the \(p\)-median problem. Discrete Optim. 8, 344–375 (2011)

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  2. Baïou, M., Barahona, F.: On the \(p\)-median polytope and the directed odd cycle inequalities: triangle-free oriented graphs. Discrete Optim. 22, 206–224 (2016)

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  3. Baïou, M., Barahona, F.: On the \(p\)-median polytope and the odd directed cycle inequalities: oriented graphs. Networks 71, 326–345 (2018)

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Author information

Authors and Affiliations

  1. CNRS and Université Clermont Auvergne, Campus Universitaire des Cézeaux, 1 rue de la Chebarde, 63178, Aubière Cedex, France

    Mourad Baïou

  2. IBM T. J. Watson research Center, Yorktown Heights, NY, 10589, USA

    Francisco Barahona

Authors
  1. Mourad Baïou
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  2. Francisco Barahona
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Corresponding author

Correspondence to Francisco Barahona .

Editor information

Editors and Affiliations

  1. CNRS and Université Clermont Auvergne, Aubière, France

    Mourad Baïou

  2. Département d'informatique et de recherche opérationnelle & CIRRELT, University of Montreal, Montréal, QC, Canada

    Bernard Gendron

  3. School of Operations Research and Information Engineering, Cornell University, Ithaca, NY, USA

    Oktay Günlük

  4. Laboratoire LAMSADE, Université Paris-Dauphine, Paris, France

    A. Ridha Mahjoub

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Baïou, M., Barahona, F. (2020). On the p-Median Polytope and the Directed Odd Cycle Inequalities. In: Baïou, M., Gendron, B., Günlük, O., Mahjoub, A.R. (eds) Combinatorial Optimization. ISCO 2020. Lecture Notes in Computer Science(), vol 12176. Springer, Cham. https://doi.org/10.1007/978-3-030-53262-8_2

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  • DOI: https://doi.org/10.1007/978-3-030-53262-8_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-53261-1

  • Online ISBN: 978-3-030-53262-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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