A class of reachability reduction problems were raised in the area of computer network security and software engineering. This paper studies such a reachability reduction problem on a vertex labeled graph. The reachability reduction here is modeled as maximum reachability preserved cut which is a variant of minimum multiway cut with a new objective function. Finding a maximum reachability preserved cut is to disconnect some labels specified in advance by edge deletion while preserving other reachable labels. It gives a way to model a large family of network problems based on graph model. We provide a comprehensive complexity analysis of this problem under different input settings. A landscape of the hardness hierarchy of this problem is shown in this paper, in which polynomial tractable and intractable cases are identified.

在计算机网络安全和软件工程领域提出了一类可及性降低问题。本文研究了顶点标记图上的这种可达性降低问题。此处将可达性降低建模为最大可达性保留切割，这是具有新目标函数的最小多向切割的变体。找到保留最大可及性的切口是在保留其他可及标签的同时，断开一些通过边删除预先指定的标签。它提供了一种基于图模型对大型网络问题进行建模的方法。我们提供了在不同输入设置下对此问题的综合复杂性分析。本文显示了该问题的硬度等级的概况，其中确定了多项式易处理和难处理的情况。