Utilizing weak graph for edge consolidation-based efficient enhancement of network robustness

Network robustness can be effectively augmented through edge safeguarding, especially when topology modification is not feasible. Although approximation algorithms are used due to the intrinsic hardness of problem, when the connectivity of the initial graph is adjusted to the desired value, the connectivity of the concealed weak graph is escalated to a maximum level. Consequently, a substantial amount of extra safeguarded edges are incorporated. To address this issue, we propose a novel concept called K-cut-segmentation that has never been used in any previous work. We then demonstrate that applying the K-cut-segmentation to the weak graph can bring connectivity of the weak graph back to the expected K. Thus, by consolidating fewer edges, the connectivity of the original graph can be maintained. The algorithm then extracts the weak graph and discovers a superior solution by constructing a partial minimum cost spanning tree. We compare the proposed algorithm with optimal and approximate algorithms across graphs of varying scales. The outcomes indicate that, for small graphs where the optimal algorithm is applicable, the algorithm achieves 100% consolidation efficacy. Solving speed is increased by up to 5 orders of magnitude, while only incurring an additional cost of approximately 3%. In large-scale graphs with one million nodes, under the same computational time, it can cut down on the consolidation cost by nearly 60% compared to existing algorithms, and the consolidation precision remains consistently high across different graph instances.