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General Variable Neighborhood Search for computing graph separators

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Abstract

Computing graph separators in networks has a wide range of real-world applications. For instance, in telecommunication networks, a separator determines the capacity and brittleness of the network. In the field of graph algorithms, the computation of balanced small-sized separators is very useful, especially for divide-and-conquer algorithms. In bioinformatics and computational biology, separators are required in grid graphs providing a simplified representation of proteins. This papers presents a new heuristic algorithm based on the Variable Neighborhood Search methodology for computing vertex separators. We compare our procedure with the state-of-the-art methods. Computational results show that our procedure obtains the optimum solution in all of the small and medium instances, and high-quality results in large instances.

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  1. http://math.nist.gov/MatrixMarket/.

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Acknowledgments

This research has been partially supported by the Spanish Ministry of “Economía y Competitividad”, Grant Ref. TIN2012-35632-C02-02.

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Authors and Affiliations

  1. Dpto. de Ciencias de la Computación, Universidad Rey Juan Carlos, Móstoles, Spain

    Jesús Sánchez-Oro & Abraham Duarte

  2. LAMIH, Université de Valenciennes, Valenciennes, France

    Nenad Mladenović

Authors
  1. Jesús Sánchez-Oro
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  2. Nenad Mladenović
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  3. Abraham Duarte
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Corresponding author

Correspondence to Abraham Duarte.

Appendix

Appendix

Tables 8 and 9 report the individual result obtained by the GVNS method. Each column shows, respectively, the vertex separator value (VS), computing time (Time) in seconds, number of vertices (\(n\)), number of edges (\(m\)), value of \(b\) and the construction parameter of the instance: node degree parameter used in the construction of the instance (N. deg.) for the Barabasi–Albert instances and the link probability parameter used in the construction of the instance (prob.) for the Erdos–Renyi instances. The maximum computing time in both sets is limited to \(0.05 \cdot n\) s. The optimum values are highlighted in bold font.

Table 8 Results on Barabasi–Albert instances
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Table 9 Results on Erdos–Renyi instances
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Sánchez-Oro, J., Mladenović, N. & Duarte, A. General Variable Neighborhood Search for computing graph separators. Optim Lett 11, 1069–1089 (2017). https://doi.org/10.1007/s11590-014-0793-z

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