A general framework for path convexities

João Vinicius C. Thompson (), Loana T. Nogueira (), Fábio Protti (), Raquel S. F. Bravo (), Mitre C. Dourado () and Uéverton S. Souza ()
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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

Journal of Combinatorial Optimization, No 0, 16 pages

Abstract: 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.

Keywords: Algorithmic complexity; Graph convexity; Path convexity (search for similar items in EconPapers)
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DOI: 10.1007/s10878-020-00618-9

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