Polynomial and pseudo-polynomial time algorithms for different classes of the Distance Critical Node Problem

We study the Distance Critical Node Problem, a generalisation of the Critical Node Problem where the distances between node pairs impact on the objective function. We establish complexity results for the problem according to specific distance functions and provide polynomial and pseudo-polynomial algorithms for special graph classes such as paths, trees and series–parallel graphs. We also provide additional insights about special cases of the Critical Node Problem variants already tackled in the literature.