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A general framework for path convexities

Author

Listed:
  • João Vinicius C. Thompson

    (CEFET/Petrópolis)

  • Loana T. Nogueira

    (Universidade Federal Fluminense)

  • Fábio Protti

    (Universidade Federal Fluminense)

  • Raquel S. F. Bravo

    (Universidade Federal Fluminense)

  • Mitre C. Dourado

    (Universidade Federal do Rio de Janeiro)

  • Uéverton S. Souza

    (Universidade Federal Fluminense)

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.

Suggested Citation

  • João Vinicius C. Thompson & Loana T. Nogueira & Fábio Protti & Raquel S. F. Bravo & Mitre C. Dourado & Uéverton S. Souza, 0. "A general framework for path convexities," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-16.
    • Handle: RePEc:spr:jcomop:v::y::i::d:10.1007_s10878-020-00618-9
    DOI: 10.1007/s10878-020-00618-9
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    References listed on IDEAS

    as
    1. Carlos V. G. C. Lima & Fábio Protti & Dieter Rautenbach & Uéverton S. Souza & Jayme L. Szwarcfiter, 2018. "And/or-convexity: a graph convexity based on processes and deadlock models," Annals of Operations Research, Springer, vol. 264(1), pages 267-286, May.
    2. Marcio Antônio Duarte & Lucia Penso & Dieter Rautenbach & Uéverton Santos Souza, 2017. "Complexity properties of complementary prisms," Journal of Combinatorial Optimization, Springer, vol. 33(2), pages 365-372, February.
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    1. João Vinicius C. Thompson & Loana T. Nogueira & Fábio Protti & Raquel S. F. Bravo & Mitre C. Dourado & Uéverton S. Souza, 2022. "A general framework for path convexities," Journal of Combinatorial Optimization, Springer, vol. 43(5), pages 994-1009, July.

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