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.

在这项工作中，我们处理在特殊路径集合上定义的所谓路径凸度。例如，图中最短路径的集合与众所周知的测地线凸度相关，而诱导路径的集合与单音凸度相关；还有很多其他例子。除了回顾文献中的路径凸度，我们还提出了一个通用的路径凸度框架，其中大多数现有的路径凸度都可以视为特殊情况。所提出的框架的一些好处是对相关问题的算法研究的系统化以及定义尚未研究的新凸面的可能性。