The Most Vital Node of the Shortest Path under Uncertainty

In an undirected, 2-nodes connected graph G(V, E) with positive real edge length, let P_G(s, t) denotes the shortest path from s to t. In this paper we focus on finding a node v* isin P_G(s, t) (other than s and t) whose removal results in the longest travel distance from s to t under uncertainty. Here we refer to uncertainty as the situation that a node failure is not known until data package travels to the adjacent node of the failure node. Such a node is defined as the most vital node of the shortest path under uncertainty (MVN-U). This paper shows that the MVN-U problem can be solved in O(n ₃) time, where n denotes the number of nodes. Finally we give an experiment of ATM networks, which demonstrates that the MVN-U problem can illustrate the realistic situation better than previous works