Employing the cluster of node cut sets to improve the robustness of the network measured by connectivity

Protection of critical nodes or edges can help defend networks from failures caused by natural disasters or intended attacks. Node protection becomes the only way when edge protection is not possible, where node connectivity is usually used to measure network robustness due to its effectiveness. Although simple, node connectivity-oriented node consolidation optimization is still NP-hard, especially when dealing with large numbers of nodes. To address the problem, by leveraging the mapping between nodes and traversal trees, per-node cluster of node cut sets is used to identify nominee nodes, which are then conditionally consolidated through a extended dual tree-based selection process. Experimental results show that in small graphs with tens of nodes where the optimal algorithm is applicable, an acceleration ratio of more than $10^5$ (at most $10^6$) is observed at the expense of about 6% extra cost. In large graphs with millions of nodes, the proposed algorithm can help promote node connectivity of more than 99.9% of node pairs, which is far better than commonly used heuristics. Its inherent ready-for-paralleling capability paves the way for more speedups.