Optimal k Cut-Sets in Attack/Defense Strategies on Networks

Abstract

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.

Attack Strategies on Networks With a Budget Constraint

“…In this section, we expose the network interdiction problem of interest to the current study. Actually, we extend previous contributions of Yaghlane et al [3], [4] and Mrad et al [2]. We will suggest a solution method that adapts to each of the three problems under consideration, as adequate, accounting for attacker resource availability as well as multiple cut-sets to target.…”

“…This article extends interdiction network models by Mrad et al [2] and Yaghlane et al [3], [4] by incorporating a budget constraint. In fact, the above studies identify optimal attack strategies without accounting for resource restrictions.…”

“…Quadros et al [32] propose a branch and cut technique to fortify n hubs recognizing that m hubs will be attacked in a way to avoid an increase in the total distribution cost. Mrad et al [2] investigate the most critical cut-sets (instead of hubs) of a network that an attacker may determine to disable the network. They develop algorithms both in the disjoint and non-disjoint cases of cut-sets to identify optimal attack strategies.…”

“…Their contribution naturally extends the min-cut problem of Yaghlane et al [4] to the most critical k cut-sets to target. While the simulation-optimization approach used in Mrad et al [2] as well as the current paper relies on the expected performance of attacks in a risk-neutral framework, some other studies incorporate the risk aversion attitudes of the antagonists particularly to avoid disastrous consequences of attacks. For instance, Song and Shen [33] use chance-constrained programming to formulate their risk-averse shortest interdiction path model.…”

“…Therefore, targeting several cut-sets seems to be more plausible to end up disabling the network. Somewhat in analogy with the identification of the k critical network hubs (discussed above), Mrad et al [2] determine using a simulation-optimization approach the critical k cut-sets to target so that to maximize the probability of a successful attack. The main shortcoming of models by Mrad et al [2] and Yaghlane et al [4] resides in ignoring the resource availability of the attacker, which is often unrealistic.…”