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The paper investigates the most critical k cut-sets to target in the context of attacks on networks. The targeted network fails if the attack successfully disables a full cut-set. The attack process is dynamic and targets one link at a time. We assume perfect information, so that the attacker picks the next link to target after identifying the outcome of the attack on the previous one. The attack may continue to reach up to k cut-sets. The problem is to identify which cut-sets to target (referred to as the k-critical cut-sets of the network) that maximize the probability of a successful attack. We distinguish both cases of disjoint and non-disjoint cut-sets. We develop an algorithm for each case with illustrations. We explore the large scale of networks and offer guidelines on the corresponding defensive strategies. INDEX TERMS cut-set, defense, interdiction networks, multiple-attacks, path-set.

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