A hierarchy of relaxation between the continuous and convex hull representations
SIAM Journal on Discrete Mathematics
Enhancing RLT relaxations via a new class of semidefinite cuts
Journal of Global Optimization
Computers and Operations Research
Detecting critical nodes in sparse graphs
Computers and Operations Research
On approximation of new optimization methods for assessing network vulnerability
INFOCOM'10 Proceedings of the 29th conference on Information communications
Robust optimization of graph partitioning and critical node detection in analyzing networks
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Deterministic network interdiction
Mathematical and Computer Modelling: An International Journal
Computational Optimization and Applications
Computers and Operations Research
Network interdiction via a Critical Disruption Path: Branch-and-Price algorithms
Computers and Operations Research
A derandomized approximation algorithm for the critical node detection problem
Computers and Operations Research
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In this paper we deal with the critical node problem, where a given number of nodes has to be removed from an undirected graph in order to maximize the disconnections between the node pairs of the graph. We propose an integer linear programming model with a non-polynomial number of constraints but whose linear relaxation can be solved in polynomial time. We derive different valid inequalities and some theoretical results about them. We also propose an alternative model based on a quadratic reformulation of the problem. Finally, we perform many computational experiments and analyze the corresponding results.