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Message: [QUOTE="JSH, post: 3597560"] Oh, the thing is you made an excellent point of where to start, and gave a great example which forced me to consider how a given start could break down with the basic algorithm, which caused me to consider a solution to that problem. That solution is to try EACH node in turn as a starting point, and calculate the path, so it doesn't matter which one your start with, so yeah, you could do it randomly. I wasn't exactly to that solution this morning but realized it a little bit later on in the day. Your example revealed though that the problem with an approach from a particular node was that there could be kind of a trap hidden far back with a steep cost, so the path from THAT node wouldn't be so great using my algorithm. But what about starting at another node? So I made the leap to just starting at each node in turn, using my algorithm to get a full path, and then comparing between to pick the best one, which would solve your simple example, but would it work on a bigger one? I think it would, as I'm conjecturing now that you cannot setup a case where from EACH node the algorithm will fail to give the optimal path, where for a graph where the costs match perfectly with distance it would give the optimal path from every node and I've designated such a graph, a perfect one. So now I'm moving to inventing terminology. I call a graph where costs match well with distance a well correlated graph, and notice your example is not one, as distances are all units, so I found a way to get my distance argument back in, with correlation. So in my terminology your example is a dis-correlated graph, where the ratio of starting points that give the optimal solution to points that do not gives the degree of correlation. James Harris [/QUOTE]

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