We investigate a two player scenario, in which a decision maker locates some facilities in a network, while a second player, called the interdictor, may disrupt the infrastructure by deleting some edges in the network in order to worsen the first player's objective value. For the case that the locational decision is assessed with the covering objective function, we show that the problem of the interdictor is NP-complete while the one of the locator is ${\mathrm{\Sigma }}_2^p$-complete. We also present a variant of the problem obtained by changing the order of the players' actions, which is shown to be ${\mathrm{\Sigma }}_2^p$-complete.

中文翻译：

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关于遮断问题的难度

我们研究了两种参与者的情况，即决策者在网络中定位了一些设施，而第二种参与者（称为拦截者）可能会通过删除网络中的某些边缘来破坏基础设施，从而使第一个参与者的客观价值恶化。对于使用覆盖目标函数评估位置决策的情况，我们证明了拦截器的问题是NP-完全问题，而定位器之一是${\mathrm{\Sigma }}_{\mathrm{2个}}^p$-完全的。我们还介绍了通过更改玩家的动作顺序而获得的问题的一种变体，这显示为${\mathrm{\Sigma }}_{\mathrm{2个}}^p$-完全的。