The problem of worst case edge deletion from a network is considered. Suppose that you have a communication network and you can delete a single edge. Which edge deletion causes the largest disruption? More formally, given a graph, which edge after deletion disconnects the maximum number of pairs of vertices, where ties for number of pairs disconnected are broken by finding an edge that increases the average shortest path length the maximum amount. This problem is interesting both practically and theoretically. In practice, it is a good tool to measure network robustness and find vulnerable edges. In theory, it is related, though subtly different, to classical problems including the dynamic all-pairs shortest paths problem, and the decremental shortest paths problem.
翻译:考虑从网络中删除最差的情况边缘的问题。 假设您有一个通信网络, 您可以删除一个边缘。 哪个边缘删除导致最大的中断? 更正式地说, 给出一个图表, 删除后最短的边缘切断了最大数量顶点的顶点, 与断开的双对的连接通过找到一个边点来增加平均最短路径长度的最大数量。 这个问题在实际和理论上都很有趣。 实际上, 它是一个用来测量网络强度和发现脆弱边缘的好工具。 在理论上, 它与传统问题有关, 包括动态全帕最短路径问题, 以及衰变最短路径问题 。