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Fuzzy Logic Augmentation of Neural and Optimization Algorithms: Theoretical Aspects and Real Applications pp 487–500Cite as

A New Heuristic Algorithm for the Vertex Separation Problem

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Part of the book series: Studies in Computational Intelligence ((SCI,volume 749))

Abstract

The Vertex Separation Problem (VSP) belongs to a family of graph layout problems. VSP consists in finding a linear ordering of the vertices of a graph such that the maximum number of vertex separators at each position of the ordering is minimized. This problem has important practical applications in fields such as very large scale integration design, computer language compiler design or natural language processing. VSP has been proven to be NP-hard. In the literature reviewed, we found several heuristic and metaheuristic algorithms designed for solving large instances of VSP. As far as we are aware, these algorithms do not use fuzzy logic. In this chapter, we adapt two fuzzy logic classifiers (FLC) to a constructive algorithm from the literature. More precisely, the first FLC is used to select the vertex to be placed at the first position of the linear ordering according to the adjacency degree. The second FLC is used to select the following vertices according to the number of vertex separators. We have designed five variants of our fuzzy heuristic. The computational experiment indicates that the first four variants have a similar behavior in solution quality and execution time.

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Acknowledgements

The first author thanks Tecnológico Nacional de México and especially Instituto Tecnológico de Altamira for their support in this research. The second author would like to thank the CATEDRAS CONACYT program.

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Authors and Affiliations

  1. Tecnológico Nacional de México, Instituto Tecnológico de Altamira, Altamira, Mexico

    Norberto Castillo-García

  2. CONACYT-Universidad Autónoma de Tamaulipas-Facultad de Ingeniería, Tampico, Mexico

    Paula Hernández Hernández

Authors
  1. Norberto Castillo-García
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  2. Paula Hernández Hernández
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Corresponding author

Correspondence to Norberto Castillo-García .

Editor information

Editors and Affiliations

  1. Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Oscar Castillo

  2. Division of Graduate Studies and Research , Tijuana Institute of Technology , Tijuana, Baja California, Mexico

    Patricia Melin

  3. Systems Research Institute, Polish Academy of Sciences , Warszawa, Poland

    Janusz Kacprzyk

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Castillo-García, N., Hernández Hernández, P. (2018). A New Heuristic Algorithm for the Vertex Separation Problem. In: Castillo, O., Melin, P., Kacprzyk, J. (eds) Fuzzy Logic Augmentation of Neural and Optimization Algorithms: Theoretical Aspects and Real Applications. Studies in Computational Intelligence, vol 749. Springer, Cham. https://doi.org/10.1007/978-3-319-71008-2_35

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  • DOI: https://doi.org/10.1007/978-3-319-71008-2_35

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-71007-5

  • Online ISBN: 978-3-319-71008-2

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