A general framework for path convexities

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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Correspondence to Uéverton S. Souza.

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This work is partially supported by Rio de Janeiro Research Support Foundation (FAPERJ) Grant Number E-26/203.272/2017, and by National Council for Scientific and Technological Development (CNPq-Brazil) Grant Number 303726/2017-2. A preliminary version of this paper appeared in AAIM 2019 (Thompson et al. 2019).

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Thompson, J.V.C., Nogueira, L.T., Protti, F. et al. A general framework for path convexities. J Comb Optim (2020). https://doi.org/10.1007/s10878-020-00618-9

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Keywords

  • Algorithmic complexity
  • Graph convexity
  • Path convexity