Monte Carlo safeguarding of key links through multiple random walks in large network

Safeguarding important links is a useful way to promote network vulnerability, especially in sparse networks where random link failures can disconnect the network. Sustaining network connectivity is the main goal of safeguarding and can be handled by selectively safeguarding links belonging to certain cuts of a network. However, due to the inherent high complexity of cut enumeration, existing algorithms can only handle small-scale networks with limited nodes. It is important to find practical algorithms that are feasible for large-scale graphs, as a significant portion of real-world graphs under investigation are not as small as dozens of nodes. To address the problem, we propose to use a high-precision approximate approach to accelerate the first step of the two-step safeguard process and thus accelerate the whole process. A Monte Carlo algorithm is proposed to exploit efficient random paths for small cuts enumeration, which can help locate important edges with high probability in large-scale sparse networks. These edges will then be utilized to find the approximated minimum cost edge set whose safeguarding can sustain the expected network connectivity. The algorithm is validated using various sizes of graphs of random/Barbasi-Albert scale-free/Clustered scale-free/unit disk/Watts-Strogatz small-world and real-world graphs. The experimental results show that the algorithm can perfectly sustain the network connectivity, and the acceleration ratio of more than 105 can be achieved with a little additional overhead. Specifically, in large graphs of one million nodes, approximated safeguard solutions survive at least 99.9% random link failures, and the solution time can be further reduced to dozens of seconds when the algorithm steps are easily implemented in full parallel.