Directed submodularity, ditroids and directed submodular flows
Directed submodularity, ditroids and directed submodular flows
复制标题
定向子模性、二重体和定向子模流
作者：
L. Qi
集合关系和诸如包含、并集和交集之类的操作被推广到有向子集，其元素区分为前向和后向元素。子模函数、拟阵和多拟阵网络流的概念被扩展到有向子模函数、二重阵和有向子集上的有向子模流的概念。两个不相关的拟阵（子模函数）可以嵌入一个二拟阵（有向子模函数）中。在这些概括中保留了总对偶完整性，并证明了非常一般的集合函数类导向的奇子模函数。
Set relations and operations such as inclusion, union and intersection are generalized to directed subsets whose elements are distinguished between forward and backward elements. The concepts of submodular functions, matroids and polymatroidal network flows are extended to the concepts of directed submodular functions, ditroids and directed submodular flows on directed subsets. Two unrelated matroids (submodular functions) can be embedded in one ditroid (directed submodular function). Total dual integrality is preserved in these generalizations and proved for very general set-function class-directed odd submodular functions.