Algorithms for the minimal cutsets enumeration of networks by graph search and branch addition

This paper presents effective algorithms for enumerating the minimal cutsets of networks. After a graph is modeled after a network, first, by a graph method the spanning tree of the graph and binary tree whose event is complement to it are evaluated. The sub-vertex set represented by the binary tree is referenced, and an algorithm which evaluates the minimal cutsets is proposed. This algorithm requires a space memorizing a topology of the graph, and has a time complexity which is proportional to a number of the edges of the graph and the binary tree. Second, by adding the branch, an algorithm enumerating the cutsets, which separates the sub-vertex set and a disjoint vertex set of the graph, is proposed. This algorithm does not enumerate all the events which the vertex and edge set can have, and executes computation to only the number of minimal cutsets. The space needed is proportional to the square of the number of the vertexes, and time complexity is in the order of the number of cutsets. The reliability is computed from the events of cutset.