The Critical Node Detection Problem in networks: A survey

In networks, not all nodes have the same importance, and some are more important than others. The issue of finding the most important nodes in networks has been addressed extensively, particularly for nodes whose importance is related to network connectivity. These nodes are usually known as Critical Nodes. The Critical Node Detection Problem (CNDP) is the optimization problem that consists in finding the set of nodes, the deletion of which maximally degrades network connectivity according to some predefined connectivity metrics. Recently, this problem has attracted much attention, and depending on the predefined metric, different variants have been developed. In this survey, we review, classify and discuss several recent advances and results obtained for each variant, including theoretical complexity, exact solving algorithms, approximation schemes and heuristic approaches. We also prove new complexity results and induce some solving algorithms through relationships established between different variants.