Simple enumeration of minimal cutsets of acyclic directed graph

A Comparison between Two All-Terminal Reliability Algorithms

“…First of all, we can revisit the formula that gives the link availabilities, (7). Imagine that a given network needs to have a certain reliability level.…”

“…In the exact case the main methods used have traditionally been either path-and cutset enumeration, which uses the inclusion-exclusion principle to obtain a value for the reliability [7], or reductions followed by a factoring process [8]. These reductions are the same as those discussed in Section II of this paper.…”

Managing the power resources of sensor networks with performance considerations

“…Much research has been done on minimal cutset formation. Yan et al [30] present a recursive labeling algorithm for determining all minimal cutsets in a directed network and [10] gives two methods for minimal cutset enumeration which use combinations of nodes. However, the main purpose of this paper is not to form the minimal cutsets but rather to schedule the off state of the request nodes.…”

Two-terminal reliability analysis for multi-phase communication networks

“…Early methods are mainly based on the enumeration of minimal paths/ cuts, or based on the factoring theory. In minimal paths/cuts methods [2,9,16,23,25,28], the reliability is evaluated by enumerating all minimal paths/cuts and summing the probabilities of their disjoint forms. A path is a set of network components (edges/vertices) such that if these components are operational, the system is up.…”