Dismantle a network efficiently during the entire process by a compound algorithm

The dismantling network problem only asks the minimal vertex set of a graph after removing which the remaining graph will break into connected components of sub-extensive size, but we should also consider the efficiency of intermediate states during the entire dismantling process, which is measured by the general performance R in this paper. In order to improve the general performance of the belief-propagation decimation (BPD) algorithm, we introduce a compound algorithm (CA) mixing the BPD and the node explosive percolation (NEP) algorithm. In this CA, the NEP algorithm will rearrange and optimize the head part of a dismantling sequence given by the BPD. Two ancestor algorithms are connected at the joint point where the general performance can be optimized. It dismantles a graph to small pieces as quickly as the BPD, and it is with the efficiency of the NEP during the entire dismantling process. We find that a wise joint point is where the BPD breaks the original graph to subgraphs no longer larger than the 1% of the original one. We refer the CA with this settled joint point as the fast CA and the fast CA is in the same complexity class with the BPD algorithm. The computation on some real-world instances also exhibits that using the fast CA to optimize the intermediate process of a dismantling algorithm is an effective approach.