Finding the Anti-block Vital Node of a Shortest Path

Let G = (V,E) be an un-directed graph with non-negative edge weights and P_G(s,t) be a shortest path between two nodes s and t where s,t belong to V(G). Suppose a package has been sent from s to t according to the route P_G(s,t) in a network modelled by the graph G. It is usual that several nodes may be not available sometimes, and one failed node is only found when its previous node of the route P_G(s,t) sends to it. In this scenario, an alternate route should be found which may lead to the increase the total length of the route. The paper discusses the problem of finding a node of the original route P_G(s,t) whose removal results in the maximum increase of the total length. We present an algorithm that runs in O(|V| + |E|log|V|) time in the worst case. In addition, some future works are also given.