Detour Admitting Short Paths

Finding the shortest path between two vertices in a weighted graph is a well explored problem and several efficient algorithms for solving it have been reported. We propose a new variation of this problem which we call the detour admitting shortest path problem (DASPP). We present an efficient algorithm for solving DASPP. This is the first algorithm that constructs a shortest path such that each edge of the shortest path admits detour with no more than k-hops. This algorithm has important applications in transportation network. We also discuss the extensions and generalizations of the proposed problem.