A novel and efficient algorithm for scanning all minimal cutsets of a graph

Abstract

We propose a novel algorithm for enumerating and listing all minimal cutsets of a given graph. It is known that this problem is NP-hard. We use connectivity properties of a given graph to develop an algorithm with reduced complexity for finding all its cutsets. We use breadth first search (BFS) method in conjunction with edge contraction to develop the algorithm. We introduce the concepts of a pivot vertex and absorbable clusters and use them to develop an enhanced recursive contraction algorithm. The complexity of the proposed algorithm is proportionate to the number of cutsets. We present simulation results to compare the performance of our proposed algorithm with those of existing methods.