1 research outputs found
Complexity of the Multilevel Critical Node Problem
In this work, we analyze a sequential game played in a graph called the
Multilevel Critical Node problem (MCN). A defender and an attacker are the
players of this game. The defender starts by preventively interdicting vertices
(vaccination) from being attacked. Then, the attacker infects a subset of
non-vaccinated vertices and, finally, the defender reacts with a protection
strategy. We provide the first computational complexity results associated with
MCN and its subgames. Moreover, by considering unitary, weighted, undirected,
and directed graphs, we clarify how the theoretical tractability of those
problems vary. Our findings contribute with new NP-complete,
-complete and -complete problems. Furthermore, for the
last level of the game, the protection stage, we build polynomial time
algorithms for certain graph classes