Network interdiction problems by deleting critical edges have wide applicatio ns. However, in some practical applications, the goal of deleting edges is difficult to achieve. We consider the maximum shortest path interdiction problem by upgrading edges on trees (MSPIT) under unit/weighted \(l_1\) norm. We aim to maximize the the length of the shortest path from the root to all the leaves by increasing the weights of some edges such that the upgrade cost under unit/weighted \(l_1\) norm is upper-bounded by a given value. We construct their mathematical models and prove some properties. We propose a revised algorithm for the problem (MSPIT) under unit \(l_1\) norm with time complexity O(n), where n is the number of vertices in the tree. We put forward a primal dual algorithm in \(O(n^2)\) time to solve the problem (MSPIT) under weighted \(l_1\) norm, in which a minimum cost cut is found in each iteration. We also solve the problem to minimize the cost to upgrade edges such that the length of the shortest path is lower bounded by a value and present an \(O(n^2)\) algorithm. Finally, we perform some numerical experiments to compare the results obtained by these algorithms.

通过删除关键边缘的网络拦截问题具有广泛的应用。然而，在一些实际应用中，难以实现删除边缘的目的。我们通过根据单位/加权\（l_1 \）范数升级树上的边缘（MSPIT）来考虑最大最短路径拦截问题。我们旨在通过增加一些边缘的权重来最大化从根到所有叶子的最短路径的长度，以使单位/加权\（l_1 \）范数下的升级成本上限为给定值。我们构建他们的数学模型并证明一些性质。针对时间复杂度为O（n）的单位\（l_1 \）范数，我们提出了针对该问题的修正算法（MSPIT ），其中n是树中的顶点数。我们提出了一种在\（O（n ^ 2）\）时间内的原始对偶算法来解决加权\（l_1 \）范数下的问题（MSPIT），其中每次迭代都找到了最小的成本削减。我们还解决了使边缘升级成本最小化的问题，以使最短路径的长度受某个值的下限限制，并提出一种\（O（n ^ 2）\）算法。最后，我们进行了一些数值实验，以比较这些算法获得的结果。