Advance Graph Algorithm

Question

Hello guys,
I am working now on a TSP(traveling salesman problem), I am facing a very challenging problem in fact.
The Main Problem: I need to find all the possible routes from A to B, I believed that there is no algorithm to provide such thing after a deadly search, so If anyone can help with just a link or a similar algorithm that would be great.
And if you are interested to know why I need such algorithm;
1 - I need to have the TSP works on only a part of a big graph, like a big city and I work the TSP only on 4 places.
2 - So I need to make a small Graph object for the only 4 places, and pass it to TSP.
3 - I need to make sure that all edges of this graph are set to the shortest paths between every pair of places. But if I found out that this shortest path go through a place which is in the TSP problem, then I have to find another(thats why i need the all routes algorithm).
4 - (which is the main problem) this short path can't pass through any place which is within the TSP problem(coz TSP go through every place only once).
(ex if the TSP is interested in places A, B, C, D and the shortest path from A to B passes through D, I can't pass this small graph object to TSP until I find another path connecting A to B and doesn't pass through C nor D -if there is no such path then of course I have to set it with infinity-).
I hope one of you guys worked on this problem before,
Thanks & Regrads,
ES_Coders

Answer 1

Thanks all,
I have already solved the problem. I will declare it again here.
TSP: is to find a cycle that goes through every node only once and goes back to the start point.
MySystem: consists of nodes from A, B, C, ...., Z.
Main Idea: user chooses a number of nodes to find their TSP.
Ex: User wants to find TSP around A, B, C only.
Problem: if the shortest path (A to B ) go through another node N, and also shortest path(B, C)go through this very same node N. Then the cycle goes through the node N twice which makes the TSP fail.
Solution:
1- Use special type of Floyed(or Dijkstra) which finds the shortest paths between every pair of nodes (n1, n2) (n1, n3) ... . But the special part is that this Floyed method takes an array of the nodes considered by TSP lets say{t1, t2, ...}. And it finds the shortest path between (n1, n2) except that this shortest path doesn't go through any of {t1, t2, t3, ...}.
2- Now when I apply TSP lets say for {A, B, C} I am sure that shortest path from (A to B) doesn't go through node C, but It can go through some other node n which doesn't belong to {A, B, C} -some other node in the system-
3- After I get my answer from TSP, if i found that this TSP doesn't pass through any place more than once, this is cool, I did it. But if it does pass through the node n more than once. (Here is the trick) I apply TSP for {A, B, C, n} by this way I ll start again whit the special Floyed making sure that every shortest path doesn't pass through n. And when I go for the real TSP the node n won't be passed through twice.
I hope I was able to declare the problem and the solution,
Thx a lot guys,
ES_Coders