In network interdiction problems, evaders (e.g., hostile agents or data packets) are moving through a network toward targets and we wish to choose locations for sensors in order to intercept the evaders. The evaders might follow deterministic routes or Markov chains, or they may be reactive, i.e., able to change their routes in order to avoid the sensors. The challenge in such problems is to choose sensor locations economically, balancing interdiction gains with costs, including the inconvenience sensors inflict upon innocent travelers. We study the objectives of (1) maximizing the number of evaders captured when limited by a budget on sensing cost and, (2) capturing all evaders as cheaply as possible.We give algorithms for optimal sensor placement in several classes of special graphs and hardness and approximation results for general graphs, including evaders who are deterministic, Markov chain-based, reactive and unreactive.A similar-sounding but fundamentally different problem setting was posed by Glazer and Rubinstein where both evaders and innocent travelers are reactive. We again give optimal algorithms for special cases and hardness and approximation results on general graphs.

中文翻译：

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Evader 拦截：算法、复杂性和附带损害

在网络拦截问题中，逃避者（例如，敌对代理或数据包）正在通过网络向目标移动，我们希望为传感器选择位置以拦截逃避者。逃避者可能遵循确定性路线或马尔可夫链，或者他们可能是被动的，即能够改变他们的路线以避开传感器。此类问题的挑战是经济地选择传感器位置，平衡拦截收益与成本，包括传感器对无辜旅行者造成的不便。我们研究了以下目标：（1）在受传感成本预算限制时最大化捕获的逃避者数量，（2）尽可能便宜地捕获所有逃避者。和一般图形的近似结果，包括确定性的、基于马尔可夫链的、反应性和非反应性的逃避者。格雷泽和鲁宾斯坦提出了一个听起来相似但根本不同的问题设置，其中逃避者和无辜的旅行者都是反应性的。我们再次给出了特殊情况下的最佳算法以及一般图上的硬度和近似结果。