Let $M=(T,C,P)$ be a security model, where T is a rooted tree, C is a multiset of costs and P is a multiset of prizes and let $(T,c,p)$ be a security system, where c and p are bijections of costs and prizes. The problems of computing an optimal attack on a security system and of determining an edge $e\in E(T)$ such that the maximum sum of prizes obtained from an optimal attack in $(T,c,p)$ is minimized when $c(e)=\infty$ are considered. An $O(G^{2}n)$-time algorithm to compute an optimal attack as well as an $O(G^2{n}^2)$-time algorithm to determine such an edge are given, in addition to a (1-ϵ) FPTAS with the time bound $O(\frac{1}{{ϵ}^2}{n}^3\log G)$ and a (1+ϵ) FPTAS with the time bound $O(\frac{1}{{ϵ}^2}{n}^4\log G)$ for the first and second problems, respectively.

让 $\mathrm{中号}=（Ť，C，P）$是一个安全模型，其中T是一棵有根的树，C是多个成本集合，P是多个奖赏集合，$（Ť，C，p）$是一个安全系统，其中c和p是成本和奖金的双射。计算对安全系统的最佳攻击并确定边缘的问题$Ë\in Ë（Ť）$ 这样，从最佳攻击中获得的最大奖金额 $（Ť，C，p）$ 被最小化 $C（Ë）=\infty$被考虑。一个$Ø（G^2ñ）$时间算法来计算最佳攻击以及 $Ø（G^2{ñ}^2）$除了带有时间限制的（1- ϵ）FPTAS外，还给出了确定这种边缘的实时算法$Ø（\frac{\mathrm{1个}}{{ϵ}^2}{ñ}^3\mathrm{日志}G）$和（1+ ϵ）FPTAS并有时间限制$Ø（\frac{\mathrm{1个}}{{ϵ}^2}{ñ}^4\mathrm{日志}G）$ 分别针对第一个和第二个问题。