EIA-CNDP: An exact iterative algorithm for critical node detection problem

Abstract

In designing reliable and impermeable networks, the robustness of the network is evaluated against the removal and failure of the node or edge where the network robustness (network connectivity) is measured using various metrics (objective functions) such as the number of connected components, size of the largest connected component, and pairwise connectivity. Critical node detection problem (CNDP) is one of the main issues in this literature, which aims to find a set of vertices whose removal maximizes or minimizes some objective function. In this paper, the focus is on solving CNDP, considering the size of the largest connected component as its objective function. In this regard, we introduce a new problem called K-Group-Division-Problem and present a mixed integer linear programming model to solve it. We prove that under certain circumstances, any optimal solution of the new problem is also an optimal solution of CNDP. Analyzing the performance of the proposed model on solving CNDP, indicates that this model is highly competitive against the base model in the literature. Furthermore, a novel exact algorithm is introduced which improves the proposed mixed integer linear programming model to address CNDP more efficiently. The results show that the proposed algorithm is much more efficient, and, compared with the base model, it can solve the problem on networks with a higher number of nodes.