How to determine if two nodes are connected?

Question

I\'m concerned that this might be working on an NP-Complete problem. I\'m hoping someone can give me an answer as to whether it is or not. And I\'m looking for more of an an

Answer 1

Your description seems to indicate that you are just interested in whether two nodes are connected, not finding the shortest path.

Finding if two nodes are connected is relatively easy:

Create two sets of nodes:  toDoSet and doneSet
Add the source node to the toDoSet 
while (toDoSet is not empty) {
  Remove the first element from toDoSet
  Add it to doneSet
  foreach (node reachable from the removed node) {
    if (the node equals the destination node) {
       return success
    }
    if (the node is not in doneSet) {
       add it to toDoSet 
    }
  }
}

return failure.

If you use a hash table or something similar for toDoSet and doneSet, I believe this is a linear algorithm.

Note that this algorithm is basically the mark portion of mark-and-sweep garbage collection.