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International Symposium on Combinatorial Optimization

ISCO 2016: Combinatorial Optimization pp 201–212Cite as

Strengthening Chvátal-Gomory Cuts for the Stable Set Problem

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9849))

Abstract

The stable set problem is a well-known \(\mathcal{NP}\)-hard combinatorial optimization problem. As well as being hard to solve (or even approximate) in theory, it is often hard to solve in practice. The main difficulty is that upper bounds based on linear programming (LP) tend to be weak, whereas upper bounds based on semidefinite programming (SDP) take a long time to compute. We propose a new method to strengthen the LP-based upper bounds. The key idea is to take violated Chvátal-Gomory cuts and then strengthen their right-hand sides. Although the strengthening problem is itself \(\mathcal{NP}\)-hard, it can be solved reasonably quickly in practice. As a result, the overall procedure proves to be capable of yielding competitive upper bounds in reasonable computing times.

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Author information

Authors and Affiliations

  1. Department of Management Science, Lancaster University, Lancaster, UK

    Adam N. Letchford

  2. Department of Information Engineering, Computer Science and Mathematics, University of L’Aquila, L’Aquila, Italy

    Francesca Marzi, Fabrizio Rossi & Stefano Smriglio

Authors
  1. Adam N. Letchford
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  2. Francesca Marzi
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  3. Fabrizio Rossi
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  4. Stefano Smriglio
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Corresponding author

Correspondence to Stefano Smriglio .

Editor information

Editors and Affiliations

  1. University of Salerno , Fisciano, Italy

    Raffaele Cerulli

  2. Kyoto University , Kyoto, Japan

    Satoru Fujishige

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

    A. Ridha Mahjoub

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© 2016 Springer International Publishing Switzerland

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Letchford, A.N., Marzi, F., Rossi, F., Smriglio, S. (2016). Strengthening Chvátal-Gomory Cuts for the Stable Set Problem. In: Cerulli, R., Fujishige, S., Mahjoub, A. (eds) Combinatorial Optimization. ISCO 2016. Lecture Notes in Computer Science(), vol 9849. Springer, Cham. https://doi.org/10.1007/978-3-319-45587-7_18

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  • DOI: https://doi.org/10.1007/978-3-319-45587-7_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45586-0

  • Online ISBN: 978-3-319-45587-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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