Max-flow min-cut theorem in an anisotropic network
Max-flow min-cut theorem in an anisotropic network
复制标题
各向异性网络中的最大流最小割定理
DOI：
10.18910/7180
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发表时间：
1990
影响因子：
0.4
通讯作者：
R. Nozawa
中科院分区：
文献类型：
--
作者：
R. Nozawa
目的是给出Rn中有界区域Ω上具有Lipschitz边界的最大流问题和最小割问题的严格形式，并证明最大流最小割定理.例如，必须给出流σ、外单位法线v、内积σ.v和割的割容的严格概念。要做到这一点，基本上遵循斯特朗的想法。Ln（Ω）中具有发散性的本质有界向量场空间和有界变差函数空间将在这一研究中发挥重要作用。实际上，静态流由前一个空间中的元素表示，静态割由属于后一个空间的特征函数表示。其中一个数学工具是广义格林公式，用于有界变差函数和L n（Ω）中具有发散性的本质有界向量场。此外，当网络是各向异性时，处理一般情况
The aim is to give rigorous formulations of max-flow problems and min-cut problems an a bounded domain Ω in R n with Lipschitz boundary and to prove max-flow min-cut theorems. For example, one has to give a rigorous notion of a flow σ, the outer unit normal v, the inner product σ.v and the cut capacity of a cut. To do so, one basically follows Strang's idea. The space of essentially bounded vector fields with divergence in L n (Ω) and the space of functions of bounded variations will play important roles in this study. In fact, a static flow is represented by an element in the former space and a static cut is represented by a characteristic function which belongs to the latter space. One of the mathematical tools is a generalized Greens' formula, for functions of bounded variation and essentially bounded vector fields with divergence in L n (Ω). Furthermore one treats the general case when the network is anisotropic