Maximum reachability preserved graph cut

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.