On the Hardness of Reachability Reduction.

A class of reachability reduction problem is raised in the area of computer network security and software engineering. We revisit the reachability reduction problem on vertex labeled graphs in which labels are representing multiple roles. In this paper, reachability reduction is modeled based on a kind of graph cut problem aiming to disconnect those reachable label pairs specified in advance by edge deletion while minimizing the number of pairs have to be disconnected, and followed by some potential applications where our model can be applied. Based on our unified model, we provide a comprehensive complexity analysis of this problem under different conditions, to provide the hardness hierarchy of reachability preserved cut problem. Result in this paper implies that reachability reduction is typically at least harder in directed graph than its undirected counterpart, even beyond NP under generalized inputs.