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 answer than just yes or no. I’d like to know why. If you can say,’This is basically this problem ‘x’ which is/is not NP-Complete. (wikipedia link)’
(No this is not homework)
Is there a way to determine if two points are connected on an arbitrary non-directed graph. e.g., the following
Well | | A | +--B--+--C--+--D--+ | | | | | | | | E F G H | | | | | | | | +--J--+--K--+--L--+ | | M | | House Points A though M (no ‘I’) are control points (like a valve in a natural gas pipe) that can be either open or closed. The ‘+’s are nodes (like pipe T’s), and I guess the Well and the House are also nodes as well.
I’d like to know if I shut an arbitrary control point (e.g., C) whether the Well and House are still connected (other control points may also be closed). E.g., if B, K and D are closed, we still have a path through A-E-J-F-C-G-L-M, and closing C will disconnect the Well and the House. Of course; if just D was closed, closing only C does not disconnect the House.
Another way of putting this, is C a bridge/cut edge/isthmus?
I could treat each control point as a weight on the graph (either 0 for open or 1 for closed); and then find the shortest path between Well and House (a result >= 1 would indicate that they were disconnected. There’s various ways I can short circuit the algorithm for finding the shortest path too (e.g., discard a path once it reaches 1, stop searching once we have ANY path that connects the Well and the House, etc.). And of course, I can also put in some artificial limit on how many hops to check before giving up.
Someone must have classified this kind of problem before, I’m just missing the name.
See http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm , your one stop shop for all graph related problems. I believe your problem is in fact solvable in quadratic time.