We consider the maximum shortest path interdiction problem by upgrading edges on trees under Hamming distance (denoted by (MSPITH)), which has wide applications in transportation network, network war and terrorist network. The problem (MSPITH) aims to maximize the length of the shortest path from the root of a tree to all its leaves by upgrading edge weights such that the upgrade cost under sum-Hamming distance is upper-bounded by a given value. We show that the problem (MSPITH) under weighted sum-Hamming distance is NP-hard. We consider two cases of the problem (MSPITH) under unit sum-Hamming distance based on the number K of critical edges. We propose a greedy algorithm within \(O(n+l\log l)\) time when \(K=1\) and a dynamic programming algorithm within \(O(n(\log n+K^3))\) time when \(K>1\), where n and l are the numbers of nodes and leaves in a tree, respectively. Furthermore, we consider a minimum cost shortest path interdiction problem by upgrading edges on trees under unit Hamming distance, denoted by (MCSPITUH) and propose a binary search algorithm within \(O(n^4\log n)\) time, where a dynamic programming algorithm is executed in each iteration to solve its corresponding problem (MSPITH). Finally, we design numerical experiments to show the effectiveness of the algorithms.

通过提升汉明距离下的树的边缘（用（MSPITH）表示），我们考虑了最大最短路径拦截问题，该问题在交通网络，网络战争和恐怖网络中都有广泛的应用。该问题（MSPITH）旨在通过升级边缘权重以使从树的根部到其所有叶子的最短路径的长度最大化，从而使总和汉明距离下的升级成本上限为给定值。我们表明，加权和-汉明距离下的问题（MSPITH）是NP-hard。我们基于临界边的数量K，在单位和-汉明距离下考虑了两种情况（MSPITH）。我们在\（O（n + l \ log l）\）中提出一个贪心算法时间时\（K = 1 \）和内的动态规划算法\（O（N（\日志N + K ^ 3））\）时\（K> 1 \） ，其中Ñ和升是数树中的节点和叶子。此外，我们考虑了通过以汉明距离为单位，以（MCSPITUH）表示的树上边缘的升级来考虑成本最小的最短路径遮断问题，并提出了在（（O（n ^ 4 \ log n）\）时间内的二进制搜索算法，其中在每次迭代中执行动态编程算法以解决其相应问题（MSPITH）。最后，我们设计了数值实验来证明算法的有效性。