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International Symposium on Combinatorial Optimization

ISCO 2014: Combinatorial Optimization pp 38–49Cite as

The Dominating Set Polytope via Facility Location

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8596))

Abstract

In this paper we present an extended formulation for the dominating set polytope via facility location. We show that with this formulation we can describe the dominating set polytope for cacti graphs, though its description in the natural node variables dimension has been only partially obtained. Moreover, the inequalities describing this polytope have coefficients in \(\{-1,0,1\}\). This is not the case for the dominating set polytope in the node-variables dimension. It is known from [1] that for any integer \(p\), there exists a facet defining inequality having coefficients in \(\{1,\ldots ,p\}\). We also show a decomposition theorem by means of 1-sums. Again this decomposition is much simpler with the extended formulation than with the node-variables formulation given in [2].

This work has been supported by project PICS05891, CNRS-IBM.

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Author information

Authors and Affiliations

  1. CNRS and Université Clermont II, Campus des Cézeaux, BP 125, 63173, 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 Mourad Baïou .

Editor information

Editors and Affiliations

  1. Univ Pierre et Marie Curie LIP6, Paris, France

    Pierre Fouilhoux

  2. Universidade de Lisboa, Lisbon, Portugal

    Luis Eduardo Neves Gouveia

  3. LAMSADE, Université Paris-Dauphine, Paris Cedex 16, France

    A. Ridha Mahjoub

  4. LAMSADE, Université Paris-Dauphine, Paris Cedex 16, France

    Vangelis T. Paschos

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© 2014 Springer International Publishing Switzerland

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Baïou, M., Barahona, F. (2014). The Dominating Set Polytope via Facility Location. In: Fouilhoux, P., Gouveia, L., Mahjoub, A., Paschos, V. (eds) Combinatorial Optimization. ISCO 2014. Lecture Notes in Computer Science(), vol 8596. Springer, Cham. https://doi.org/10.1007/978-3-319-09174-7_4

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  • DOI: https://doi.org/10.1007/978-3-319-09174-7_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09173-0

  • Online ISBN: 978-3-319-09174-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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