In p-median location interdiction the aim is to find a subset of edges in a graph, such that the objective value of the p-median problem in the same graph without the selected edges is as large as possible. We prove that this problem is NP-hard even on acyclic graphs. Restricting the problem to trees with unit lengths on the edges, unit interdiction costs, and a single edge interdiction, we provide an algorithm which solves the problem in polynomial time. Furthermore, we investigate path graphs with unit and arbitrary lengths. For the former case, we present an algorithm, where multiple edges can get interdicted. Furthermore, for the latter case, we present a method to compute an optimal solution for one interdiction step which can also be extended to multiple interdicted edges.

翻译：在p-中位点选址阻断问题中，目标是在图中找到一个边的子集，使得同一图中移除选定边后p-中位点问题的目标值尽可能大。我们证明即使对于无环图，该问题也是NP难的。将问题限制在边长为单位长度、单位阻断成本且仅阻断单条边的树上时，我们提出了一种多项式时间内求解该问题的算法。进一步地，我们研究了具有单位长度和任意长度的路径图。对于前者，我们提出了一种可阻断多条边的算法；对于后者，我们提出了一种计算单次阻断最优解的方法，该方法也可推广至多条边被阻断的情况。