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A General Framework for Path Convexities

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Algorithmic Aspects in Information and Management (AAIM 2019)

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Abstract

In this work we deal with the so-called path convexities, defined over special collections of paths. For example, the collection of the shortest paths in a graph is associated with the well-known geodesic convexity, while the collection of the induced paths is associated with the monophonic convexity; and there are many other examples. Besides reviewing the path convexities in the literature, we propose a general path convexity framework, of which most existing path convexities can be viewed as particular cases. Some benefits of the proposed framework are the systematization of the algorithmic study of related problems and the possibility of defining new convexities not yet investigated.

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Author information

Authors and Affiliations

  1. Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, Rio de Janeiro, Brazil

    João Vinicius C. Thompson

  2. Universidade Federal Fluminense, Niterói, Brazil

    João Vinicius C. Thompson, Loana T. Nogueira, Fábio Protti, Raquel S. F. Bravo & Uéverton S. Souza

  3. Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil

    Mitre C. Dourado

Authors
  1. João Vinicius C. Thompson
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  2. Loana T. Nogueira
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  3. Fábio Protti
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  4. Raquel S. F. Bravo
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  5. Mitre C. Dourado
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  6. Uéverton S. Souza
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Corresponding author

Correspondence to Uéverton S. Souza .

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Editors and Affiliations

  1. The University of Texas at Dallas, Richardson, TX, USA

    Ding-Zhu Du

  2. Hefei University of Technology, Hefei, China

    Lian Li

  3. Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China

    Xiaoming Sun

  4. Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China

    Jialin Zhang

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Thompson, J.V.C., Nogueira, L.T., Protti, F., Bravo, R.S.F., Dourado, M.C., Souza, U.S. (2019). A General Framework for Path Convexities. In: Du, DZ., Li, L., Sun, X., Zhang, J. (eds) Algorithmic Aspects in Information and Management. AAIM 2019. Lecture Notes in Computer Science(), vol 11640. Springer, Cham. https://doi.org/10.1007/978-3-030-27195-4_25

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  • DOI: https://doi.org/10.1007/978-3-030-27195-4_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-27194-7

  • Online ISBN: 978-3-030-27195-4

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