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

TL;DR

This paper introduces a new algorithm that efficiently enumerates all minimal cutsets of a graph by leveraging connectivity properties, BFS, and edge contraction, significantly reducing complexity compared to existing methods.

Contribution

The paper presents a novel recursive contraction algorithm utilizing pivot vertices and absorbable clusters to improve enumeration of minimal cutsets.

Findings

The proposed algorithm reduces enumeration complexity proportional to the number of cutsets.

Simulation results show improved performance over existing methods.

The algorithm effectively leverages graph connectivity properties for efficiency.

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.