A note on shortest path problems with forbidden paths

Abstract

We consider the variant of the shortest path problem in which a given set of paths is forbidden to occur as a subpath in an optimal path. We establish that the most-efficient algorithm for its solution, a dynamic programming algorithm, has polynomial time complexity; it had previously been conjectured that the algorithm has pseudo-polynomial time complexity. Furthermore, we show that this algorithm can be extended, without increasing its time complexity, to handle non elementary forbidden paths.

Application of Graph Theory in Grain and Oil Deployment

“…In this situation, we add s as the virtual source point, and s represents the deployment warehouse. 6 as the reserve station. We add t as a virtual point to the network graphics.…”

“…[5] tried to find an answer to the question of which shortest path algorithm for the one-to-one shortest path problem ran fastest on a large real-road network and solved the key problem of the computation of shortest paths between different locations on a road network, which appeared in many applications. [6] considered the variant of the shortest path problem in which a given set of paths was forbidden to occur as a subpath in an optimal path, established that the most-efficient algorithm for its solution, a dynamic programming algorithm, had polynomial time complexity, and showed that this algorithm could be extended, without increasing its time complexity, to handle non elementary forbidden paths. [7] investigated the time-dependent reliable shortest path problem, which was commonly encountered in congested urban road networks.…”