Is there an algorithm to compute the shortest Hamiltonian path in an undirected graph from one point to another in polynomial time? Assumptions:


given a graph with N nodes, and two specific nodes A and B
the  graph is undirected and no edge has a negative cost
there exists at least one Hamiltonian path with A and B as an end points


Is there a way to find the shortest path from A to B that passes through all the other points? 

Note: I'm only concerned with the specific given nodes A and B as endpoints, thus there's no need to compute for other Hamiltonian paths with different endpoints.

I'm thinking if it's possible to modify Dijkstra's shortest path algorithm to find Hamiltonian paths. Is it possible? If so, how? If not, is there any other algorithm that can be used? (in polynomial time)
The case you are describing is NP-complete, so the answer is no. 

I don't know if still remains NP-complete if the graph is a Euclidean graph. Anyone knows?