Efficient Network Dismantling via Node Explosive Percolation

The network dismantling problem asks the minimum separate node set of a graph whose removal will break the graph into connected components with the size not larger than the one percentage of the original graph. This problem has attracted much attention recently and a lot of algorithms have been proposed. However, most of the network dismantling algorithms mainly focus on which nodes are included in the minimum separate set but overlook how to order them for removal, which will lead to low general efficiency during the dismantling process. In this paper, we reformulate the network dismantling problem by taking the order of nodes' removal into consideration. An efficient dismantling sequence will break the network quickly during the dismantling processes. We take the belief-propagation guided decimation (BPD) dismantling algorithm, a state-of-the-art algorithm, as an example, and employ the node explosive percolation (NEP) algorithm to reorder the early part of the dismantling sequence given by the BPD. The proposed method is denoted as the NEP-BPD algorithm (NBA) here. The numerical results on Erdös-Rényi graphs, random-regular graphs, scale-free graphs, and some real networks show the high general efficiency of NBA during the entire dismantling process. In addition, numerical computations on random graph ensembles with the size from $2^{10}$ to $2^{19}$ exhibit that the NBA is in the same complexity class with the BPD algorithm. It is clear that the NEP method we used to improve the general efficiency could also be applied to other dismantling algorithms, such as Min-Sum algorithm, equal graph partitioning algorithm and so on.