A Note on the Complexity of Sliding Shortest Paths

We address a shortest path problem in a given uncapacited and undirected network N=(V,E) with positive edge costs. In addition we are given a single source-destination pair (s,t), a shortest path p{st} connecting s and t and a new edge e =(p,q). The task is to find a minimum number of edges Ec and the minimum weight increase for each edge e in Ec such that the shortest path p{st} between s and t traverses edge e. We show that the problem is NP-hard and give a heuristic scheme for the problem

A Note on the Complexity of Sliding Shortest Paths

We address a shortest path problem in a given uncapacited and undirected network N=(V,E) with positive edge costs. In addition we are given a single source-destination pair (s,t), a shortest path p{st} connecting s and t and a new edge e =(p,q). The task is to find a minimum number of edges Ec and the minimum weight increase for each edge e in Ec such that the shortest path p{st} between s and t traverses edge e. We show that the problem is NP-hard and give a heuristic scheme for the problem